In the proof of theorem 2 we determined the quantity exx -

Question

In the proof of Theorem 2 we determined the quantity E[X(X - 1)], called the second factorial moment. In general, the rth factorial moment of X is given by

Express μ'₂, μ'₃, and μ'₄ in terms of factorial moments. 1

Theorem 2

The mean and the variance of the binomial distribution are