考研 设随机变量X1,X2,X3相互独立,且有X1~b(4,1/2),X2~b(6,1/3),X3~b(6,1/3),求E(X1-X2),E(X1-2*X2)这个怎么做
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数学期望具有线性性,有：
(1)E(X+Y) = EX + EY.并且不必要求X,Y独立
(2)E(aX + b) = aEX + b
根据X1, X2, X3的分布,有
E(X1) = 4 * 1/2 = 2
E(X2) = 6 * 1/3 = 2
E(X3) = 6 * 1/3 = 2
所以E(X1 - X2) = E(X1) - E(X2) = 2 - 2 = 0
E(X1 - 2 * X2) = E(X1) - 2 * E(X2) = 2 - 2 * 2 = -2