Let XXX be binomially distributed X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). Under what condition is E[X2]=Var(X)+(E[X])2E[X^2] = Var(X) + (E[X])^2E[X2]=Var(X)+(E[X])2 always true?
Never
Always
When p=0.5p = 0.5p=0.5
When np(1−p)=(np)2np(1-p) = (np)^2np(1−p)=(np)2