Let X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). Find the expected value of X2(X−1)X^2(X-1)X2(X−1).
n^2(n-1)p^3
n(n−1)(n−2)p3n(n-1)(n-2)p^3n(n−1)(n−2)p3
n(n−1)(n−2)p3+n(n−1)p2n(n-1)(n-2)p^3 + n(n-1)p^2n(n−1)(n−2)p3+n(n−1)p2
n(n−1)p2n(n-1)p^2n(n−1)p2