If the mean and variance of a binomial variable X are 2 and 1 respectively, then P ( X >1)=

Step-by-step solution

Mean =2 n p=2 aligned & and Variance =1 n p q=1 & 2(1-P)=1 2-2 p=1 & p=1 / 2 aligned 1 2 n=2 n=4 aligned & Now, P(X>1)=1-P(X 1) & =1-P(X=0)-P(X=1) aligned aligned & =1- ^4 C ₀ p ^0 q ⁴⁻⁰- ^4 C _ i pq ^3 & =1-1.1 ( 1 2 )^4 4 1 2 1 2^3 & P ( X 1)= 15 16 - 4 16 = 11 16 aligned