BINOMIAL DISTRIBUTIO

N

Probability Distribution of a Discrete Random Variable

BINOMIAL DISTRIBUTION Binomial distribution is related to Bernoulli trial – an experiment which has only two possible outcomes, success or failure.

P(X=r) = nCr pr qn-r

where,p is the probability of successq is the probability of failure (q=1-p)r is the number of success

TO DETERMINE WHETHER A VARIABLE HAS A BINOMIAL DISTRIBUTION: The number of trials, n must be fixed Each trial can result in only one of two outcome – success or failure The probability of a success in a single trial is a constant Each trial is independent

TABLE OF BINOMIAL DISTRIBUTION Table 1 in Statistial table booklet

MEAN AND VARIANCE OF A BINOMIAL DISTRIBUTION

X ~ B (n,p)

Mean: E(x) = np Variance: Var(x) = npq Standard deviation: