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IIBF has released the New Syllabus Exam Pattern for CAIIB Exam 2023. Following the format of the current exam, CAIIB 2023 will have now four papers. The CAIIB Rural Banking includes an important topic called “Issues Concerning Rural Areas”. Every candidate who are appearing for the CAIIB Certification Examination 2023 must understand each unit included in the syllabus.
In this article, we are going to cover all the necessary details of CAIIB Rural Banking Module A Unit 7 : Issues Concerning Rural Areas, Aspirants must go through this article to better understand the topic, Issues Concerning Rural Areas and practice using our Online Mock Test Series to strengthen their knowledge of Issues Concerning Rural Areas. Unit 7 : Issues Concerning Rural Areas
Rural development has several components such as increase in production of agriculture, allied activities and non-farm sector, increase in the income of the poor, generation of employment opportunities particularly for the poor, and provision of basic amenities and infrastructural facilities such as health, education, drinking water, good roads, electricity and market centers.
Community Average:
Rural Development program in India, started with Community Development Program (CDP) which was launched in the year 1952. It was a broad- based program covering agriculture, animal husbandry, irrigation, co-operation, village and small- scale industries, health, education, communication and housing.
The aim was to secure total development of material and human resources, thus, promoting social welfare and social justice and also building up of the democratic organization of the people.
Growth-oriented Approach:
Food shortage during the Second Plan period shifted the focus on augmenting food grains production.
Program like the Intensive Agriculture District Program (IADP), the Intensive Cattle Development Program (ICDP), the High Yielding Varieties Program (HYVP) were launched in the 60s. The focus of these programs was on increased production. This approach, however, helped only the rich farmers in rural areas, but failed to make any dent in the basic problem of poverty and unemployment.
Target Group Approach:
The Small Farmers Development Agency (SFDA) and Marginal Farmers and Agricultural Labourers (MFAL) Agency were introduced with the hope of increasing the income of small farmers, marginal farmers and agricultural labourers.
Several employment generation programs such as Food for Work Program, National Rural Employment Program (NREP), Rural Landless Employment Guarantee Program (RLEGP) and Jawahar Rozgar Yojana (JRY) were initiated, in a phased manner. The target group approach proved more effective in delivering the benefits of development programs to the poor.
Area Development Approach:
Several area-specific programs were introduced for the development of backward areas in the 70s. They were Drought Prone Area Program (DPAP), Desert Areas Development Program (DDP), Hill Area Development Program (HADP) and Tribal Area Development Program (TADP). It proved successful in reducing inter-regional disparities by promoting the development of backward areas.
Welfare Approach:
Under this segment, welfare programs like Minimum Needs Program and Applied Nutrition Program were introduced by the Government in order to provide basic public services to the rural people.
Integrated Rural Development Approach:
This was designed to achieve balance among growth, removal of poverty and employment generation with focus on target groups to help small and marginal farmers, agricultural labourers and rural artisans.
This strategy took an integrated view of rural poverty and unemployment and addressed economic, commercial, organization, technological and political bases of these problems.
The successful implementation of this strategy required integration of economic activities of rural families by developing all the three sectors – primary, secondary and tertiary.
The sustainable rural development would mean the development for the present generation, without compromising the ability of the future generation to meet its own needs. Causes of ecological imbalance in rural areas are as follows:
Land and Water Mismanagement: Land and water are two important natural resources. The quality of environment lies in efficient use of land and water. Proper management of land has not been paid proper attention in most part of the country. This is posing a major threat to progress in rural areas. Water logging and consequent salinity in irrigated areas due to lack of proper drainage facilities has affected about 6 million hectares of land in the country.
Destruction of Other Natural Living Resources: India’s other natural living resources including animals, plants and other marine ecosystems are immense. Due to the pressure of population and other developments, the habitats of species are undergoing change which has resulted into disappearance of certain species and ecosystems.
National Mission for Sustainable Agriculture (NMSA):
NMSA has been made operational by GOI from the year 2014-15 which aims at making agriculture more productive, sustainable, remunerating and climate resilient
Soil Health Management (SHM):
It aims at promoting Integrated Nutrient Management (INM), through judicious use of chemical fertilizers including secondary and micro nutrients in conjunction with organic manures and bio-fertilizers, for improving soil health and its productivity; strengthening of soil and fertilizer testing facilities.
Pradhan Mantri Krishi Sinchayee Yojana (PMKSY):
It is implemented by GOI to achieve convergence of investments in irrigation at the field level, expand cultivable area under assured irrigation, improve on-farm water use efficiency to reduce wastage of water, enhance the adoption of precision-irrigation and other water saving technologies (more crop per drop).
The Paramparagat Krishi Vikas Yojana
It is implemented with the aim to promote organic cultivation in India, to improve soil health as well as organic matter content and to boost the net income of the farmer so as to realize premium prices.
National Agriculture Market
It gives an e-marketing platform at the national level and support creation of infrastructure to enable e-marketing. This new market process is revolutionizing agriculture markets by guaranteeing better price discovery. It has also facilitated bringing in transparency and competition to enable cultivators to get improved remuneration for their produce moving towards ‘One Nation One market’.
Pradhan Mantri Fasal Bima Yojana (PMFBY)
Providing financial support to farmers suffering crop loss/damage arising out of unforeseen events
Stabilizing the income of farmers to ensure their continuance in farming
Encouraging farmers to adopt innovative and modern agricultural practices and
Ensuring credit worthiness of the farmers, crop diversification and enhancing growth and competitiveness.
The issues concerning rural development in our country are briefly indicated below:
Backwardness
Agricultural growth rate was not high in India and it could not increase income of agriculturists significantly. Moreover, the growth was not the same for all the crops and all the regions. Fluctuation in rainfalls affects agricultural production and leads to fluctuation in the income of farmers.
Massive Poverty
The large number of rural poor is mostly landless labourers, small and marginal farmers and rural artisans, as they either have no assets or the assets owned by them, have low productivity. The major reasons of poverty are to be found in the social and economic structure, prevailing in the rural areas.
Large Scale Unemployment
The level of unemployment in agricultural sector is very high as most of the people engaged in agriculture are in disguised unemployment, as the number of workers is larger than the need for them.
Poor Basic Infrastructure Obtaining in Rural Areas
Basic infrastructural facilities such as roads, electricity, drinking water, schools, hospitals, transport and communication in rural areas are inadequate and poorly maintained. As a result, the poor villagers do not get proper education and remain in the vicious cycle of poverty.
Small and Unorganized Rural Entrepreneurs
Since most rural entrepreneurs are small and unorganized, they have a low bargaining power, in terms of processing raw material and marketing of produce. This results in exploitation of rural producers.
Traditional Farming Techniques
Government intervention is required to bring more and more area under modern methods of production so that the agriculture production can increase and there is improvement in income level of farmers.
Inadequate Support for Agriculture
Supporting services for agriculture such as transport, storage, processing and marketing facilities are inadequate. The marketing infrastructure need to be further augmented, if diversification of agriculture and export of agriculture products need to be intensively promoted.
Rural Indebtedness
Rural people were mainly depending upon money lenders, for meeting their credit requirement. Moneylenders exploited the farmers in a number of ways.
Urban-Oriented Development
Most of the heavy industries both in public and private sector have come up in urban areas because of the availability of infrastructural facilities and backward and forward linkages in these centres and so the benefits from this growth have also accrued mainly to the urban population.
Migration of Rural Population to Urban Centres
A large part of rural population migrates to urban areas every year, mainly in search of jobs. Very high percentage of urban migrants are poor and landless for whom, work opportunities in rural areas are limited/ negligible.
Rural-Urban Linkages
Rural and urban areas play complimentary role in the overall economic development. Improvement of rural areas is important for its role as suppliers of raw materials and labour to industry and as consumer of industrial products.
Development is defined as the process by which, the members of a society increase their personal and institutional capacities to mobilize and manage resources, to produce sustainable and justly distributed improvements in quality of life consistent with their own aspirations.
Rural development means overall development of rural areas, with a view to improving the quality of life of the rural people. It includes development of agriculture and allied activities, village and cottage industries, socio-economic infrastructure, community services and above all, human resources in rural areas.
Sustainable Development
The World Commission on Environment and Development (The Brundtland Commission) defined sustainable development as the development that meets the needs of the present, without compromising the ability of future generation to meet their own needs.
Organizing for Rural Development
The major question here is as to how to design and maintain effective organizations for rural development. Indian experience showed that the government organizations became bureaucratic, lacked responsiveness and entailed considerable leakages. Participation of people was lacking, resulting in dismal performance of the programs.
Facilitating Rural Development
Facilitating rural development would involve leading, motivating, monitoring and controlling aspects of rural development management. Facilitation component of rural management would involve three major areas viz. human resources development, infrastructure development and policy support.
The agricultural marketing involves three essential components – assembling, processing and distribution.
Objectives of Rural Marketing: The objectives of rural marketing can be summarized as: (a) to give the best possible benefit for primary producers, such as, farmers and household industries; (b) to make available all rural products in the desired form and quality at reasonable prices and in adequate measure; (c) to reduce price spread between primary producers and ultimate consumers.
Characteristics of Agricultural Produce: Perishability, Seasonality of Production, Bulkiness of Products, Variation in Quality of Production, Small Size and Scattered Production, Processing, Consumption Characteristics, Price Inelasticity
Deficiencies in the Agricultural Marketing System
Exploitation by middle men
Wide Price Spread
Distress Sale
Inadequate Storage
Transportation Cost
Absence of Grading and Standardization
Lack of Market Intelligence
Malpractices
Capacity Building in Agricultural Marketing
Agricultural Produce Market Committee (APMC) Act
Agricultural markets in the country are regulated by state Agricultural Produce Marketing Committee (APMC)
Under these state Acts, farmers are required to sell their produce at state-owned mandis. APMC mandis currently levy a market fee on farmers who wish to sell their produce in the mandis. This makes it expensive for farmers to sell at APMC mandis. In addition, farmers have to arrange for their produce to be transported from their farms to the nearest mandi, which brings in costs such as transport and fuel. In transporting the produce from the farm to the store, several intermediaries are involved.
The central government had released a Model APMC Act in the year 2003, suggesting its enactment by the states.
The Model Act provides for
The direct selling of produce through contract farming,
Permitting private persons, farmers and consumers to establish agricultural markets,
Levying a single market fee on the sale of the commodity, and
Replacing licenses with registration of market agencies, so that they can operate in more than one market, among other things.
Launching of eNAM: During the year 2016, GOI has launched the National Agricultural Market (NAM)- the electronic market, for providing opportunities to farmers for selling their produce for better price. The electronic portal, under the auspices of NAM project (eNAM), is managed by Small Farmers’ Agribusiness Consortium (SFAC). In the eNAM platform, farmers can opt to trade directly on their own through the mobile app or through registered commission agents.
Developments in the recent years:
Amendments to the APMC Act by State Governments: With the amendment of the APMC Act by the states, establishment of Electronic Spot Markets that allow online trading through electronic commodity exchanges have become
Pledge Loan linked to Warehouse receipts: Availability of finance against stored produce and improved knowledge on price risk management allows farmers and farmers’ organizations to obtain better price realization for their produce.
E-Trading: The following categories of virtual market (a) Futures Exchange (b) Spot Exchange (c) Warehouse Receipt System (d) ICT based Market Information and (e) Web Marketing provide the needed width and depth to the market.
Grading and Standardization: The government has passed an act ‘Agricultural Produce (Grading and marketing) Act’, which empowers the Central Government to prescribe grade standards for agricultural commodities and livestock products.
The Directorate of Marketing and Inspection (DMI) have prepared grade standards, for a number of agriculture commodities. Graded agriculture products bear the AGMARK The Central Quality Control Laboratory at Nagpur and its regional subsidiaries in various places collect samples of products from market, analyze them for chemical and physical properties, for the purpose of grading.
Use of Standard Weight: The passing of standard Weight Act and adoption of metric system, facilitated uniformity and enforcement of standard weight, all over the country.
Storage facilities: After agricultural produce is harvested, it requires a robust storage infrastructure in order to minimize any losses due to adverse weather conditions or in the process of transportation.
Initiatives for integration of production, processing and marketing: Integration of production, processing, marketing is required for agricultural produce marketing, to facilitate prosperity of the rural producers.
Introduction of Negotiable Warehouse Receipt System: The Negotiable Warehouse Receipts (NWRs), issued by the warehouses, registered under this Act, would help the farmers to avail loan from banks against NWRs and the NWRs will become a prime tool of trade. This will avoid distress sale of agricultural produce by the farmers in the peak marketing season when there is glut in the market.
GATT and Agricultural Marketing
Government of India has taken a number of steps to promote international trade such as decentralization, liberalization of credit facilities and substantial reduction of tariffs. Probably, the most significant milestone is the signing of General Agreement on Trade and Tariff (GATT) by India along with 121 other countries, in December 1992, after the Uruguay round of talks.
TRIPS is the most comprehensive international agreement on IP and it has a major role in enabling trade in creativity and knowledge, in resolving trade disputes over intellectual property, and in assuring WTO members the latitude to achieve their domestic policy objective.
Agriculture Price Policy
Based on the recommendations of the Committee on Food grains Price, the Agricultural Prices Commission was set up in the year 1965, which was renamed as Commission for Agricultural Costs and Prices (CACP) in the year 1985. The Commission is expected to evolve a balanced and integrated price structure with due regard to the interests of both producers and consumers, and advise the Government of India on price policy of agricultural commodities.
Minimum Support Price
Based on the recommendations of the CACP, the Department of Agriculture and Co-operation, Government of India, declares Minimum Support Price (MSP) for 24 crops before the sowing season. The idea behind MSP is to give guaranteed prices and assured market to the farmers and save them from the price fluctuations.
It insulates farmers from the unwarranted fluctuation in prices, caused by the variation in supply lack of market integration, information asymmetry and other elements of market imperfection plaguing the agricultural markets. The guaranteed price and assured market are expected to encourage higher investment and in adoption of modern technologies in agricultural activities.
Other Pricing Mechanisms
Statutory Minimum Prices: They are like minimum support prices. It is legally binding on the buyer to purchase the commodity at the announced price or higher. Statutory minimum prices are applicable to crops such as sugarcane.
Procurement Prices: The price at which the government procures food grains or industrial raw material for maintenance of buffer stocks, feeding the public distribution system, is called the procurement price.
Issue Prices: These are the prices at which, government provides certain specified commodities in the minimum needed quantity to the consumers through public distribution agencies like ration shops and fair price shops. They are generally lower than market prices.
Procurement option
Price Support Operations: The Government agencies remain in readiness in the market and in the event of prices tending to fall below the support price, the farmers voluntarily offer their produce to the Government agencies. No target for procurement is fixed. The objective of procurement is to provide price support to the farmers.
Open Market Purchase: The Government agency enters the market like any other trader and purchases the required quantities in competition with the traders.
Pre-emptive Purchase: The Government reserves the first right of purchase at the price settled in the open market. The Government agency does not participate in the competitive bidding. When the price for a lot is settled, the Government agency has the right to step in and buy the given quantity at the price settled.
Monopoly Procurement: In this method of procurement, the Government reserves the right of purchase from the farmers. The traders are not allowed to enter the market for purchase and sale. This method of procurement is adopted only when other methods fail.
Buffer Stocks: A buffer stock of food grains refers to the stocks maintained by the Government, to cushion the shocks of fluctuations in supply and prices. The main advantages of maintaining buffer stocks of food grains are to impart stability to the food economy; reduce fluctuations in the income of food grains producers; stabilize the prices of food grains for consumers; and use it to save people from hunger, at the time of scarcity.
IIBF has released the New Syllabus Exam Pattern for CAIIB Exam 2023. Following the format of the current exam, CAIIB 2023 will have now four papers. The CAIIB Paper 1 (Advanced Bank Management) includes an important topic called “Theory of Probability”. Every candidate who are appearing for the CAIIB Certification Examination 2023 must understand each unit included in the syllabus.
In this article, we are going to cover all the necessary details of CAIIB Paper 1 (ABM) Module A (Statistics ) Unit 6 : Theory of Probability, Aspirants must go through this article to better understand the topic, Theory of Probability and practice using our Online Mock Test Series to strengthen their knowledge of Time Series. Unit 6 : Theory of Probability
Probability means chance/s or possibility of happening of an event. For example, suppose we want to plan for a picnic in a weekend.
Before planning we may check the weather forecast and see what is the chance that there will be rain at that time, accordingly we may do the planning.
Probability gives a numerical measure of this chance or possibility.
Suppose it says that there is a 60% chance that rain may occur in this weekend, 60% or 0.6 is called the probability of raining. To understand the concept of probability first we have to understand the concepts of Factorial, Permutations and Combinations.
Factorial:
In mathematics, Factorial is equal to the product of all positive integers which are less than or equal to a given positive integer. The Factorial of an integer is denoted by that integer and an exclamation point.
Thus, factorial five is written as 5! which is equal to 1 × 2 × 3 × 4 × 5 = 120
The product of the first n natural numbers is called factorial n and is denoted by n! =
n × (n – 1) × (n – 2) × … × 2 × 1
The above formula can also be represented as n! = n × (n – 1) … (n – r + 1) × (n – r)!
Where r < n It may be noted that:
0! = 1, 1! = 1
Permutations and Combinations
A permutation is the arrangement of objects in which order is the priority. The fundamental difference between permutation and combination is the order of objects, in permutation, the order of objects is very important, i.e., the arrangement must be in the stipulated order of the number of objects, taken only some or all at a time.
The combination is the arrangement of objects in which order is irrelevant. The notation for permutation is P (n, r) or nPr, denoting the number of permutations of n things when r things are selected at a time.
If there are three things a,b, and c then permutations of three things taken two at a time is denoted by P (3, 2) or 3P2.
It is given by (a, b), (a, c), (b, c), (b, a), (c, a), (c, b) = 6
In general,
P (n, r) is the number of permutations when r things are selected at a time from n items.
The notation for combination is C(n, r) or nCr which is the number of combinations or selections of n things if only r things are selected. If there are three things a, b and c then combination of these three things taken two at a time is denoted by 3C2 and is given by (a, b), (a, c), (b, c) = 3
Example: Using 5 letter of word SHYAM, how many distinct word can be formed?
N= 5
R= 5
5P5 = 5!/ (5-5)! = 5*4*3*2/0! = 5*4*3*2/1 = 120
Note: Permutation and Combination are related to each other by formula P(n,r) = r! * C(n,r).
Example: In how many ways 3 pencils can be selected from 5 pencils?
3 pens can be selected from 5 pens in 5C3 ways
5C3 = 5! / 3! 2! × = 10 ways
Example: From a group of 7 boys and 6 girls, 3 boys and 4 girls is to be selected. In how many ways this can be done?
3 boys can be selected from 7 boys in 7C3 ways
= 7C3 = 7! /3! 4! ×
= 7* 6 *5 *4! /3*2*4! = 35
4 girls can be selected from 6 girls in 6 C4 ways
= 6! 4! 2! = 6 *5 *4! /4! *2 = 15
3 boys and 4 girls can be selected in 7C3 × 6C4 = 35 × 15 = 525 ways.
Random Experiment or Trial
An operation or experiment conducted under identical conditions and which has a number of possible outcomes is called Random Experiment or Trial.
Example: 1. Tossing a coin 2. Throwing a dice 3. Selecting a card form a pack of cards
Sample Space and Sample Points
The set of all possible outcomes of a random experiment is called sample space.
The elements of the sample space are called sample points. Sample space is denoted by S.
Example: 1. In an experiment of throwing a coin, S = {H,T]
In an experiment of throwing a dice, S = {1, 2, 3, 4, 5, 6}
The number of sample points in a sample space of random experiment is denoted by n (s).
For example, (1) n (S) = 2, and
example (2) n (S) = 6
Event
Any subset of the sample space S is called an event.
If S is a sample space and A is a subset of S (i.e., A⊂ S), then A is called an event.
Example: In an experiment of throwing dice where S = {1, 2, 3, 4, 5, 6}, the event of getting odd numbers is A = {1, 3, 5}
Types of Events
Certain Event
If sample points in an event are same as sample points in sample space of that random experiment, then the event is called a certain event.
Example: Getting any number between 1 to 6 on a dice is a certain event.
Impossible Events
An event which never occurs or which has no favourable outcomes is called an impossible event. In other words, the event corresponding to the set φ (null set) is called an impossible event.
Example: Getting a number 7 on a dice is an impossible event.
Mutually Exclusive Events
Events are said to mutually exclusive if the happening of any of them restricts the happening of the others i.e., if no two or more of them can happen together or simultaneously in the same trial.
Example: In tossing a coin event head and tail are mutually exclusive. Note: If A & B are mutually exclusive events of sample space S, then A ∩ B = φ.
Example: In tossing a coin event head and tail are mutually exclusive. Note: If A & B are mutually exclusive events of sample space S, then A ∩ B = φ.
Equally Likely Events
Events are said to be equally likely if they have equal choice to occur. In other words, outcomes of a trial are said to be equally likely if taking into consideration all relevant evidences, there is no reason to prefer one with respect to other.
Example: In throwing a dice all the six faces are equally likely to occur.
Exhaustive Events
If the sample points of the events taken together
Note: If A & B are exhaustive events of sample space S, then A U B = S.
Example: Random Experiment:
Throwing a dice S = {1,2,3,4,5,6},
A= Event of odd numbers = {1, 3, 5}
B= Event of odd numbers = {2, 4, 6},
C= Event of multiple of 3 = {3, 6}
Here A U B = {1, 2, 3, 4, 5, 6} = S,
Here A and B are called exhaustive events
But A U C = {1, 3, 5, 6} ≠ S,
so A and C are not exhaustive events.
Complementary Event
If A is an event in sample space S, then the non-occurrence event of A is called Complementary event of A.
Two events A and B are called complementary events, if A and B exhaustive as well as mutually exclusive events.
In other words, A and B are called complementary events if
A U B = S and A ∩ B = φ.
Example: Random Experiment: Throwing a dice, S = {1, 2, 3, 4, 5, 6}, A = {1, 2}, B = {3, 4, 5, 6} As A U B = S and A ∩ B = φ, A and b are complementary events.
Complementary event of A is denoted by Ac, A/ or A.
If the sample space S of a random experiment consists of n equally likely, exhaustive and mutually exclusive sample points and m of them are favourable to an event A, then the probability of event A is given by
Number of favourable items/ Total number of outcomes
Example: Two unbiased dice are thrown. Find the probability that:
Both the dice show same number.
First dice shows 6.
The total of the numbers on the dice is 8.
Solution In a random throw of two dice, the total number of cases is given below:
A: Both the dice show same number
n(A)/n(S) = 6/36 = 1/6
B: First die show 6 n(B)/n(S) = 6/36 = 1/6
C: Total of the number
on the dice is 8 n(C)/n(S) = 5/36
Example: Two unbiased coins are tossed simultaneously. Find the probability of getting –
at least one tail,
majority of heads
S = {(H, H), (H, T), (T, H), (T, T)}
n (S) = 4
(i)A: At least one tail,
P (A) = n (A)/ n (S) = 3 /4
(ii)B: Majority of heads
P (B) = n (B)/ n( S) = 1/ 4
Addition Theorem
Let A and B are two events (subsets of sample space S) and are not disjoint, then the probability of the occurrence of A or B or A and B both, in other words probability of occurrence of at least one of them is given by,
Example: Find the probability that a card drawn from a pack of cards will be a red or a picture card.
Probability of selecting a red card = 26 = Event A
P(A) = 26/52 = 1/2
Probability of getting picture card = 6 = Event B
P(B) = 12/52 = 3/13
There are 6 red cards which are picture cards,
P (A∩B) = 6/52
P (A U B) = P (A) + P (B) – P (A∩B)
½ + 3/13 – 6/52 = 8/13
The conditional probability of an event A is the probability that the event will occur given the knowledge that an event B has already occurred.
P (A/B).
If the events A and B are such that the occurrence of A doesn’t depend upon occurrence of event B, (A and B are independent event), the conditional probability of event A given event B is simply the probability of event A, that is P (A).
Similarly, probability of event B given that event A has already occurred is denoted by P (B/A).
P (B/A) = P (A ∩ B) / P(A)
Example: Consider a fair coin is tossed 3 times
S = (HHH, HHT, HTH, TTT, TTH, THT, THH, HTT) = 8
Event A = Atleast two tail appear
Event B – First coin show Head
P(A) = (TTT, TTH, THT, HTT) = 4/8 = ½
P(B) = (HHH, HHT, HTH, HTT) = 4/8 = ½
P (A ∩ B) = 1/8
P(A/B) = 1/ 8 / ½ = 1/4
Multiplication Theorem
If A and B are two events of a sample space S associated with an experiment, then the probability of simultaneous occurrence of events A and B is given by
P (A ∩ B) = P(A) P(B/A) = P(B) P(A/B)
Independent Events
Two events A and B are independent of each other if the occurrence or non-occurrence of one does not affect the occurrence of the other.
P (A ∩ B) = P(A) P (B)
Example: Two balls are drawn from a bag one by one with 2 white and 3 black balls. What is the probability that the second ball is white?
Event W1 = first ball – White Ball
Event B1 = First Ball – Black Ball
Event W2 = Second Ball – White Ball
1st White Ball = 2/5 + ¼
2nd Black Ball = 3/5 + 2/4
P(W2) = P(W1) + P(W2/W1) + P(B1) + P(W2/B1)
2/5 + ¼ + 3/5 + 2/4= 2/5
A random variable is a function that associates a real number with each element in the sample space.
In other words, a random variable is a function X: S → R,
where S is the sample space of the random experiment under consideration and R is the real number line.
Example. Consider the random experiment of tossing a coin two times and observing the result (a Head or a Tail) for each toss.
Let X denote the total number of heads obtained in the two tosses of the coin.
Example: Suppose that you play a certain lottery by buying one ticket per week. Let X be the number of weeks until you win a prize. X is a random variable.
Discrete Random Variable:
If a random variable takes a finite number or countable infinite number of possibilities, it is called a discrete random variable.
Example: 1. Age in years 2. Number of arrivals in a clinic 3. Number of accidents
Continuous Random Variable:
If a random variable takes infinite number of possibilities, it is called a continuous random variable.
Example 1. Percentage of marks 2. Weight 6.5 PROBABILITY
Consider a random experiment consisting of n repeated independent trials with p the probability of success at each individual trial. Let the random variable X represent the number of successes in the n repeated trials.
Then X follows a Binomial distribution.
The definition of this distribution is:
A random variable X has a binomial distribution,
X ~ Binomial (n, p), if the discrete density of X is given by:
P[X=x] = f(x) = nCx px (1 – p)n–x,
x = 0, 1, 2…, n = 0 otherwise
f(x) = nCx px qn–x;
x = 0, 1, 2…, n = 0 otherwise where p + q = 1
P = the probability of success
n is the total number of trials.
Example: Toss a coin for 10 times and you wan to get head 4 times & probability of coming head is 0.5 calculate f(x)?
n = 10, x= 4 & p = 0.5
q = 1- 0.5 = 0.5
f(x) = nCx px qn–x
= 10C4* 0.510 o.510
Many instances of binomial distributions can be found in real life.
If a new drug is introduced to cure a disease, it either cures the disease (it’s successful) or it doesn’t cure the disease (it’s a failure).
If you purchase a lottery ticket, you’re either going to win money, or you aren’t. Basically, anything you can think of that can only be a success or a failure can be represented by a binomial distribution.
Mean = np
Variance = np (1 – p) = npq
SD = √ variance
Measure of Skewness = â1 = (1-2p)2/npq
Measure of Kurtosis = â2 = 3 + [1 – 6pq /npq]
Binomial Distribution is symmetric if p = q = 0.5
If p < 0.5, distribution is positively skewed and
if p > 0.5, distribution is negatively skewed.
M= (n+1) p
If M is not an integer, mode is the integral part lying between M – 2 and M.
If M is an integer, there are two modes and thus the distribution is bimodal, and two modes are M – 1 and M.
Problem: If X follows Binomial distribution with n = 8, p = 1/2, then Find P [IX-4I ≤ 2]
Solution : P[-2<=(X-4)<=2]
P[2<= X<=6]
P[2<= X<=6] = P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)
f(x) = nCx px qn–x = 8Cx 1/2x 1/28–x
8Cx 1/2x 1/28–x =
= 8C2 1/22 1/28–2 + 8C3 1/23 1/28–3 + 8C4 1/24 1/28–4 + 8C5 1/25 1/28–5 + 8C6 1/26 1/28–6
= (1/2)8 (8C2 + 8C3 + 8C4 + 8C5 + 8C6)
= 1/256 (128+ 56+ 70 +56 +28) = 119/128
The Poisson probability distribution was introduced by S. D. Poisson.
A random variable X, taking on one of the values 0, 1, 2,…, is said to be a Poisson random variable with parameter λ, λ > 0, if its probability mass function is given by
The symbol e stands for a constant approximately equal to 2.7183. It is a famous constant in mathematics, named after the Swiss Mathematician L. Euler, and it is also the base of the so-called natural logarithm
Some examples of Poisson probability are:
The number of misprints on a page (or a group of pages) of a book.
The number of people in a community living to 100 years of age
The number of wrong telephone numbers that are dialed in a day.
The number of transistors that fail on their first day of use.
The number of customers entering a post office on a given day.
Mean = λ,
Variance = λ
Measure of Skewness = β1 = 1 /λ
Measure of Kurtosis β2 = 3 +1/λ
Mode: If l is not an integer mode is the integral part lying between λ–1 and λ
If λ s an integer, there are two modes and thus the distribution is bimodal and two modes are λ −1 , λ
Problems. Births in a hospital occur randomly at an average rate of 1.8 births per hour.
What is the probability of observing 4 births in a given hour at the hospital?
What about the probability of observing more than or equal to 2 births in a given hour at the hospital?
Let X= No. of births in a given hour = 4 with Mean rate λ = 1.8
e-1.8 = .16529
f(x) = e-1.8 * 1.84 /4!
.16529 * 10.4976/ 24 = 0.0723
(ii) We want P(X ≥ 2) = P(X = 2) + P(X = 3) +…, i.e., an infinite number of probabilities to calculate
but P(X ≥ 2) = P(X = 2) + P(X = 3) +… = 1 − P(X < 2)
= 1 − (P(X = 0) + P(X = 1)
= 1 − (0.16529 + 0.29753) = 0.538
A normal distribution is a distribution that occurs naturally in many situations where 50% of the data will fall to the left of the mean and 50% will fall to the right.
For example, Height of the population, most of the people in a specific population are of average height. The number of people taller and shorter than the average height people is almost equal, and a very small number of people are either extremely tall or extremely short.
Some other examples are distribution of Income in economy, distribution of marks in an exam, etc.
A random variable X is said to follow Normal Distribution if its pdf is given by
Note:
µ and σ2 are called parameters of Normal Distribution.
If µ = 0 and σ2 = 1, then the Normal variable is called Standard Normal Variable. Generally, it is denoted by Z.
The graph of Normal Distribution is bell shaped and symmetric.
Quartile deviation is 0.6745σ
Mean deviation is 0.7979σ
Mean = Median = Mode = µ
Problem: Normal population of 1000 employees has mean income Rs. 800 per day and variance 400, Find no. of employees where income between [ P(Z= 1) = 0.3413, P(Z= 2) = 0.4772 & P(Z= 2.5) = 0.4938 P(Z= 5) = 0.5]
P (750 < x < 820)
P (x > 700)
P (x > 760)
n= 1000 , µ= 800 & σ2 = 400
Z = X- µ /σ
i)X = 750 = 750- 800/ 20 = 2.5 = 0.4938
X = 820 = 820-800 / 20 = 1 = 0.3413
= 0.4938 + 0.3413 = 0.8351 = 83.51%
ii)X = 700 = 700 – 800/ 20 = 5 = 0.5
0.5 + 0.5 = 1 = 1000 employees
n= 1000 , µ= 800 & σ2 = 400
Z = X- µ /σ
iii) X = 760 = 760-800/20 = 2 = 0.4772
0.4772 + 0.5 = 0.9772
We can apply probability concept and different formulas and laws of probability in different practical field.
One very important application is Credit Risk.
When lenders offer mortgages, credit cards, any type of loan to different customers, there could be a risk that the customer or borrower might not repay the loan.
Similarly, if a company extends credit to a customer, there could be a risk that the customer might not pay their invoices.
We are interested to calculate this risk of not repaying any due payment. This is called Credit Risk.
Credit risk also represents the risk that a bond issuer may fail to make a payment when requested, or an insurance company will not be able to pay a claim.
Thus, Credit Risk is the possibility or chance or probability of a loss occurring due to a borrower’s failure to repay a loan to the lender or to satisfy contractual obligations. It refers to a lender’s risk of having its cash flows interrupted when a borrower does not repay the loan taken from him.
There are three types of credit risks.
Credit default Risk :
Credit default risk is the type of loss that is incurred by the lender either when the borrower is unable to repay the amount in full or when 90 days pass the due date of the loan repayment. This type of credit risk is generally observed in financial transactions that are based on credit like loans, securities, bonds or derivatives.
Concentration Risk:
Concentration risk is the type of risk that arises out of significant exposure to any individual or group because any adverse occurrence will have the potential to inflict large losses on the core operations of a bank. The concentration risk is usually associated with significant exposure to a single company or industry or individual.
Country risk
The risk of a government or central bank being unwilling or unable to meet its contractual obligations is called Country or Sovereign Risk.
When a bank or financial institution or any other lender has an indication that the borrower may default the loan payment, he will be interested to calculate the expected loss in advance.
The expected loss is based on the value of the loan (i.e., the exposure at default, EAD) multiplied by the probability, that the borrower will default (i.e., probability of default, PD).
In addition, the lender takes into account that even when the default occurs, it might still get back some part of the loan.
Hence, PD * EAD is further multiplied by the estimation of the part of the loan which will be lost in case that a default occurs (i.e., loss given default, LGD).
Expected loss = PD * EAD * (1 – LGD)
Problem: Let a credit of Rs. 2,000,000 was extended to a company one year ago. Determine the expected loss for the exposure if the company defaults completely, where the loss given default is 50%.
Probability of default, PD = 100
Loss given default, LGD = 50%
Expected loss = 100% * Rs. 2,000,000 * (1 – 50%)
= Rs. 1,000,000
The concept of value at risk is associated with portfolio of an individual or an organisation.
A portfolio is a collection of different kinds of assets owned by an individual or organisation to fulfil their financial objectives.
One can include fixed deposit or any investment where he or she can earn a fixed interest, equity shares, mutual funds, debt funds, gold, property, derivatives, and more in his portfolio.
In any type of investment where one can earn fixed interest are not risky, but risk is associated with the investments in Equity market, Mutual Funds, Gold, etc.
Value at risk (VaR) is a financial metric that one can use to estimate the maximum risk of an investment over a specific period.
If the portfolio value is Rs. 30,000 and if 1-month average return and standard deviation is 10% and 12% respectively, calculate daily VaR at 95% confidence level.
VAR at 95% confidence level
= [Return of the portfolio –1.65 *σ][ Value of the portfolio]
= [0.1–1.65*0.12] *30000
= [0.1 –0.198] *30000 = –2940 = 9.8% of the portfolio
Pradhan Mantri Kisan Samman Nidhi (PM-KISAN). The scheme aims to provide a payment of Rs. 6,000 per year, in three 4-monthly installments of Rs. 2,000 to the farmers families
Pradhan Mantri Kisan Maan Dhan Yojana (PM-KMY) for providing old age pension to these farmers. Under this Scheme, a minimum fixed pension of Rs. 3,000 will be provided to the eligible small and marginal farmers, on attaining the age of 60 years.
Government has approved the increase in the Minimum Support Price (MSPs) for all Kharif & Rabi crops for 2018-19 season, at a level of at least 150 percent of the cost of production.
“Per drop more crop” initiative under which drip/sprinkler irrigation is being encouraged for optimal utilization of water, reducing cost of inputs and increasing productivity
“Paramparagat Krishi Vikas Yojana (PKVY)” launched for promoting organic farming.
Launch of e-NAM initiative to provide farmers an electronic transparent and competitive online trading platform.
Under “Har Medh Par Ped”, agro-forestry is being promoted for additional income. With the amendment of Indian Forest Act, 1927, Bamboo has been removed from the definition of trees. A restructured National Bamboo Mission has been launched in the year 2018 to promote bamboo plantation on non-forest government
Government has approved a new Umbrella Scheme ‘Pradhan Mantri Annadata Aay Sanrakshan Abhiyan (PM-AASHA)’. The Scheme is aimed at ensuring remunerative prices to the farmers for their produce.
Bee keeping has been promoted under Mission for Integrated Development of Horticulture (MIDH) to increase the productivity of crops through pollination and increase the honey production as an additional source of income of farmers.
Government provides interest subvention of 2 per cent on short-term crop loans up to Rs. 3.00 lakh besides incentive for prompt repayment at 3 per cent. Presently, loan is available to farmers at an interest rate of 4 per cent per annum on prompt repayment.
There are Micro Irrigation Fund (Rs. 5,000 crores); Agri-marketing Fund to strengthen eNAM and GrAMs (Rs. 2,000 crores); Agricultural Infrastructure Fund (AIF) to build agri-logistics (backward & forward linkages) (Rs. 1 lakh crore).
Market intervention scheme: The Department of Agriculture, Cooperation and Farmers’ Welfare implements the MIS for procurement of agricultural and horticultural commodities which are perishable in nature and are not covered under the PSS. The objective of intervention is to protect the growers of these commodities from making distress sale in the event of a bumper crop during the peak arrival period when the prices tend to fall below economic levels and cost of production.
Government of India has launched the scheme “Deendayal Upadhyaya Gram Jyoti Yojana” for rural electrification to provide continuous power supply to rural India in 2015. The erstwhile Rajiv Gandhi Grameen Vidyutikaran Yojana (RGGVY) scheme for village electrification and providing electricity distribution infrastructure in the rural areas has been subsumed in the DDUGJY.
Rural Electrification Corporation is the Nodal Agency for implementation of the DDUGJY.
Under the scheme, 60% of the project cost (85% in the case of special states) is provided as grant by GOI and additional grant up to 15% (5% in the case of special category states) is provided on achievement of prescribed milestones.
The International Energy Agency (IEA), 2018 has acknowledged that India’s move to energize every village in the country with electricity is one of the greatest success stories in the world in 2018.
A centrally sponsored scheme of Integrated Dry Land Agricultural Development was launched in 1970-71, in 24 pilot projects. The objective of the scheme was to test and demonstrate the technology developed by the All -India Co-ordinated Research Project for Dryland Agriculture, under the Indian Council for Agricultural Research (ICAR).
The major components of watershed development were:
Land development,
Construction of water harvesting storage,
Coverage of area with improved/drought resistant seeds and fertilizers.
The National Watershed Development Project for Rainfed Areas (NWDPRA) initiated in the Sixth Plan envisaged that a micro watershed would be taken up for development in every block having assured irrigation of less than 30%.
Soil conservation is a measure undertaken in order to prevent soil loss from erosion or reduced fertility, caused by over usage, acidification, salinization or other chemical soil contamination.
Techniques adopted for improved soil conservation include practices like crop rotation, cover cropping, conservation tillage and planted windbreaks (linear planting of trees and shrubs in a designed way), etc.
The National Water Policy (NWP), 2012 serves as a policy guideline, for development and management of water resources, in the country.
It has emphasized on their implementation through the National Water Board, by preparing a plan of action. The Ministry of Water Resources, River Development and Ganga Rejuvenation, is responsible for conservation, management and development of water, research and development, training and matters relating to irrigation and multi-purpose projects
Pradhan Mantri Krishi Sinchayee Yojana (PMKSY)
It is being implemented with the objective of developing a long- term solution for mitigating the effect of drought and increasing area under irrigation with motto of ‘Har Khet Ko Pani’.
The scheme has been conceived amalgamating the Accelerated Irrigation Benefit Program (AIBP) of the Ministry of Water Resources, River Development & Ganga Rejuvenation (MoWR, RD&GR), Integrated Watershed Management Program (IWMP) of Department of Land Resources (DoLR) and the On Farm Water Management (OFWM) of Department of Agriculture, Cooperation and Farmers Welfare.
The major objective of PMKSY is to achieve convergence of investments in irrigation at the field level, expand cultivable area under assured irrigation, improve on farm water use efficiency to reduce wastage of water, enhance the adoption of precision irrigation and other water saving technologies.
The Fund was instituted with an initial corpus of Rs. 2,000 crore, by way of deposits to be placed with NABARD by commercial banks to the extent of their respective shortfalls in agriculture lending, under priority sector.
At present, there are 37 eligible activities under RIDF as approved by GOI. The eligible activities are classified under three broad categories i.e.,
Agriculture and related sector
Social sector and
Rural connectivity.
The project for rural connectivity, social and agri-related sector, are eligible for loans to the extent of 80% to 95% of project cost.
Loans availed under RIDF are to be repaid in equal annual instalments within seven years from the date of withdrawal, including a grace period of two years. The interest shall be paid at the end of each quarter. The implementation phase for projects sanctioned under the Fund is spread over two to five years, varying with the type of the project and also location of the state.
Macroeconomic Stabilization
The key policy reforms introduced in this area were fiscal-monetary policy reforms. These were aimed at:
Providing a better balance between aggregate demand and supply
Minimizing the distortion effects of the tax system
Forcing public enterprises to minimize cost and maximize efficiency.
Government’s expenditure was concentrated in two areas:
Consumption expenditure, and
Subsidy payments.
In order to generate additional revenue, government planned to broaden tax base, rationalize tax rates and improve collection through non-tax sources.
Structural Reforms
Comprehensive structural reforms have been undertaken to improve the supply-side of economy. Among them the important ones were: (i) Trade and capital flows reforms, (ii) Industrial deregulation, and (iii) Public sector reforms.
Trade and Capital flow Reforms:
Government initiated a number of trade policy changes, with a view to integrating the Indian economy better, with the rest of the world. The value of rupee was adjusted downward by about 20 per cent in July 1991.
The other measures included the convertibility of the rupee first on trade account and then on entire current account transaction, liberalization of import regime, substantial lowering in customs tariff rates, measures to promote exports.
Industrial Deregulation:
Historically, domestic economic activities in India were subjected to a wide-ranging government control measure. In the industrial sector, such controls took various forms like industrial licensing, which acted as a barrier to entry, reservation of a large number of industries, for the public sector and for the small-scale sector, time consuming procedures required for the exit of firms from an industry and price and distribution control on various industrial products. The thrust of new industrial policy announced in July, 1991 was on removing these controls
Public Sector Reforms
Since the public sector was not generating enough internal resources and becoming a constraint on economic growth, the government adopted a new approach viz. provision of greater managerial autonomy to public enterprises to enable them to work efficiently; encourage private sector competition in areas where social considerations are not paramount; and provide market orientation to the public sector through the disinvestment process.
A committee under the chairmanship of Shri M. Narasimham was set up to examine the country’s Financial System and the committee submitted its report in December 1991. The Committee, recommended
Gradual reduction of the reserve requirements to be maintained by banks (both SLR and CRR)
Redefining the priority sector and phasing out the directed lending programs
Interest rate determination on the grounds of market forces such as demand for and the supply of fund
Structural reorganization of the banking sector
Establishment of ARF tribunal, to ease the problems of NPAs in banks
Provision of autonomy to the public sector banks
Adoption of uniform accounting practices, particularly, in regard to income recognition and provisioning against doubtful assets and making full disclosures in the balance sheets
Rationalization of operations of foreign banks.
Following acceptance of the report by GOI, the following actions were initiated:
SLR and CRR were reduced from 38.5 per cent to 25 per cent and from 15 per cent to 10 per cent respectively.
The RBI introduced prudential norms for income recognition, classification of assets and provisioning for bad debts for the first time.
The banks were required to maintain capital equivalent to 8 per cent of their risk weighted assets.
Commercial banks which had met certain stipulated conditions were allowed to open new branches without the approval of the RBI. They were also permitted to close down non-viable branches other than those in rural and semi-urban areas.
Interest rates of commercial banks on loans above Rs. 2 lakhs were fully deregulated.
Interest rates on advances of all Co-operative banks and Regional Rural Banks were deregulated.
The impact of reforms on rural economy is discussed in the following five important areas
Flow of credit for agriculture and rural development
Investment in agriculture
Input subsidies
Agricultural exports
Poverty alleviation and employment generation programs