If the mean and the variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than one is equal to

Step-by-step solution

aligned & Mean =2 and variance =1 & np =2 and npq =1 & npq np = 1 2 q = 1 2 & p =1- 1 2 = 1 2 & n p=2 & n ( 1 2 )=2 n =4 aligned array ll & P(X 1) & =P(X=2)+P(X=3)+P(X=4) array = ^4 C ₂ ( 1 2 )^2 ( 1 2 )^2+ ^4 C ₃ ( 1 2 )^3 ( 1 2 )+ ^4 C ₄ ( 1 2 )^4 ( 1 2 )^0 aligned & =6 ( 1 2 )^4+4 ( 1 2 )^4+1 ( 1 2 )^4 & = 1 2^4 (6+4+1)= 11 16 aligned