x C p , x q n q otherwise … = − , , , .. ; Any random variable which follows binomial distribution is known as binomial variate i.e X ~ B ( n , p ) is a binomial variate. Note The Binomial distribution can be used under the following conditions : . The number of trials ‘ n ’ finite .
The trials are independent of each other. . The probability of success ‘ p ’ is constant for each trial. .
In every trial there are only two possible outcomes – success or failure. Derivation of the Mean and Variance of Binomial distribution : The mean of the binomial distribution E(X) = n x x n x p q = p n x q = np ( q + p ) n – [since p + q = ] = np E ( X ) = np ∴ The mean of the binomial distribution is np Var ( X ) = E ( X ) – { E ( X )} XII Std - Business Maths & Stat EM Chapter - - Probability Distributions Here E ( X ) = n x x p q n x x x x p q