Quantitative
Quantitative techniques may be defined as those techniques which provide the decision makes a systematic and powerful means of analysis, based on quantitative data,Quantitative techniques may be defined as those techniques which provide the decision makes a systematic and powerful means of analysis, based on quantitative data There are different types of quantitative techniques. We can classify them into three categories. They are: Mathematical Quantitative Techniques Statistical Quantitative Techniques Programming Quantitative Techniques Functions : To facilitate the decision-making process 2. tools for scientific research 3. helpoptimal strategy 4.proper deployment of resources 5. minimizing costs 6. Limitations : : . involves maths and equations , inolves number and careful , expensive , don’t take intangible factors
Probability refers to the chance of happening or not happening of an even/The probability of given event may be defined as the numerical value given to the likely hood of the occurrence of that event. It is a number lying between ‘0’ and ‘1’ ‘0’ denotes the even which cannot occur, and ‘1’ denotes the event which is certain to occur. For example, when we toss on a coin, we can enumerate all the possible outcomes (head and tail), but we cannot say which one will happen. Hence, the probability of getting a head is neither 0 nor 1 but between 0 and 1. It is 50% or ½
A random experiment is an experiment that has two or more outcomes which vary in an unpredictable manner from trial to trail when conducted under uniform conditions.
Sample Point Every indecomposable outcome of a random experiment is called a sample point. It is also called simple event or elementary outcome/ When a die is thrown, getting ‘3’ is a sample point.
Sample space of a random experiment is the set containing all the sample points of that random experiment. When a coin is tossed, the sample space is (Head, Tail)
A set of events are said to be mutually exclusive of the occurrence of one of them excludes the possibiligy of the occurrence of the others.
A group of events is said to be exhaustive events when it includes all possible outcomes of the random experiment under consideration.
Priori Approach If out of ‘n’ exhaustive, mutually exclusive and equally likely outcomes of an experiment; ‘m’ are favourable to the occurrence of an event ‘A’, then the probability of ‘A’ is defined as to be m/n the probability is the ratios of the number of favourable cases to the total number of equally likely cases.” P(A) = Total number of favorable cases / total number of equally likely cases
Addition Therom : If two events, ‘A’ and ‘B’, are mutually exclusive the probability of the occurrence of either ‘A’ or ‘B’ is the sum of the individual probability of A and B. P(A or B) = P(A) + P(B) i.e., P(AB) = P(A) + P(B)
If two events, A and B are not mutually exclusive the probability of the occurrence of either A or B is the sum of their individual probability minus probability for both to happen. P(A or B) = P(A) + P(B) – P(A and B) i.e., P(AB) = P(A) + P(B) – P(A∩B)
Multiplication Therom : )Multiplication theorem (dependent Events):- If two events, A and B are dependent, the probability of occurring 2nd event will be affected by the outcome of the first. P(AתB) = P(A).P(B/A)
Baye’s Theorom : Baye’s theorem is based on the proposition that probabilities should revised on the basis of all the available information. The revision of probabilities based on available information will help to reduce the risk involved in decision-making. The probabilities before revision is called priori probabilities and the probabilities after revision is called posterior probabilities. According to Baye’s theorem, the posterior probability of event (A) for a particular result of an investigation (B) may be found from the following formula:- P (A/B) = P (A) P(B) / P(A) P(B) + P (Not A) P B/Not A
Probability distribution (Theoretical Distribution) can be defined as a distribution obtained for a random variable on the basis of a mathematical model. It is obtained not on the basis of actual observation or experiments, but on the basis of probability law.
Binomial distribution is the probability distribution expressing the probability of one set of dichotomous alternatives, i.e., success or failure. In other words, it is used to determine the probability of success in experiments on which there are only two mutually exclusive outcomes. Binomial distribution is discrete probability distribution. Binomial Distribution can be defined as follows: “A random variable r is said to follow Binomial Distribution with parameters n and p if its probability function is: P (x) = nCx p^x q ^n-x n= total number p = probability of success q – proability of failure
Poisson Distribution is a limiting form of Binomial Distribution. In Binomial Distribution, the total number of trials are known previously. But in certain real life situations, it may be impossible to count the total number of times a particular event occurs or does not occur. In such cases Poisson Distribution is more suitable. Poison Distribution is a discrete probability distribution. It was originated by Simeon Denis Poisson. The Poisson Distribution is defined as p(x) = e^-m c m^x / x!