Covariance of binomial distribution

Question

Suppose X~ binomial (n, p). Then cov(X, n-X) is

A. np(1-p)

B.-np(1-p)

C. np(1-p)²

D.-np(1-p)²

Answer 1

Since X ~ Binomial(n, p), then Var(X) = np(1 - p). Thus

 

cov(X, n - X) = cov(X, n) - cov(X, X) = 0 - Var(X) = -np(1 - p) 

 

and the answer is (B).