Let X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). Find the expected value of the random variable X(n−X)X(n - X)X(n−X).
n(n−1)p(1−p)n(n-1)p(1-p)n(n−1)p(1−p)
n2p(1−p)n^2 p(1-p)n2p(1−p)
n(n+1)p(1−p)n(n+1)p(1-p)n(n+1)p(1−p)
n(n-1)p^2