PRESTIGE

INSTITUTE OF MANAGEMENT , GWALIOR

Submitted by: RAHUL KAPOLIYAMBA-1ST C

Submitted to :PROF. AMRITA SHRIVASTAVA

BINOMIAL DISTRIBUTION

Uses of binomial distributionThe binomial distribution can be used when :

The outcomes or results of each trial in the process are characterized as one of two types of possible outcomes. In other words, they are attributes.

The possibility of outcome of any trial does not change and is independent of the results of previous trials.

Conditions for the applicability of binomial distributionFor the applicability of binomial distribution in an experiment, the following conditions must be satisfied :

The experiment is performed for a finite and fixed number of trials.

The trials do not depend on each other. Each trial must surely result in either a success or

a failure. The probability of success in each trial is the

same.

Obtaining coefficients of the binomialFor obtaining coefficients from the binomial expansion, the following rules may be remembered.To find the terms of the expansion of (q+p)—The first term is qn

— The second term is nC1qn-rp —In each succeeding term the power of q is reduced by 1 and

the power of p is increased by 1.—The coefficient of any term is found by multiplying the

coefficient of the preceding term by the power of q in that preceding term, and dividing the products so obtained by one more than the power of p in that preceding term.

when we expend (q+p) , we get (q+p)n = qn + nC1qn-1p + nC2qn-2p2 + ………………….. nCrqn-rpr

Properties of the binomial distribution The shape and location of binomial distribution changes as p

changes for a given n or as n changes for a given p. As p increases for a fixed n, the binomial distribution shifts to the rights.

The mode of the binomial distribution is equal to the value of x which has the largest probability.

As n increases for a fixed p, the binomial distribution moves to the right and spreads out. The mean of the binomial distribution, np, obviously increases as n increases with p held constant.

Assumption of binomial distributionTrials are repeated

All trials should be independent

The number of trial (n) should be fixed

There are two mutually exclusive outcomes in each trial, success and failure.