Use linearity of expectation to devise an alternative method of proving the formula E[X] = np where X b(n, p). (Hint See Exercise 2.) Solution A binomial (n,p) random variable can be viewed as a sum of n independent bernoulli trials i. e rv s with distribution bernoulli(p) So if X~bin(n,p) then X=X1 +X2 +...Xn Where Xi ~ bernoulli(p) Hence E(Xi )=p hence E(X)=E (Xi )= E(Xi ) ( By linearity of expectation ) =np.