Let X be a random variable with binomial probability distribution with number of trials n and probability of success p. Prove the following: 1. The expectation of X is, E(X) = n.p 2. The variance of X is, σ^(2) = Var(X) = n.p.q 3. The standard deviation of X is, σ = √Var(X) = √n.p.q where q is the probability of failure such that q = 1 - p.​