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

Step-by-step solution

aligned & Mean = np =2 and variance = npq =1 & q = 1 2 aligned aligned & Also, p=1-q=1- 1 2 = 1 2 & n =4 aligned aligned P(X 1) & =1-P(X=0) & =1- ^4 C₀ p^0 q^4 & =1-(1) ( 1 2 )^0 ( 1 2 )^4 & =1- 1 16 & = 15 16 aligned