例4.1.1 X~B(n,p),求E(X) 解: E(X kCnP(1-p)ê✐❆✍❺❆✍➻ê ê➷Ï✧ ➅➴❈þ✛➄☛❺■❖☛ ❫❻ê➷Ï✧ ⑦4.1.1 X ∼ B(n, p), ➛E(X) . ✮: E(X) = Xn k=0 kCk np k (1 − p) n−k = np Xn k=1 (n − 1)! (k − 1)!(n − k)! p k−1 (1 − p) (n−1)−(k−1) = np nX−1 k=0 C k n−1p k (1 − p) (n−1)−k = np ❆⑦ ❡Y ∼ B(1, p), ❑E(Y ) = p Ü ★ ✮ ❱➬Ø➘✿