如题所述
令:Z = X + Y;
应用方差的定义:D(Z) = E{[Z-E(Z)]²} 和X,Y的独立性,
D(Z) = D(X+Y) = E{(X+Y)² - [E(X)+E(Y)² ]} = E[X² - E²(X)] + E[Y² - E²(Y)] +
+ E[2XY] - 2E(X) E(Y) = D(X) + D(Y) + 0
即: D(X+Y) = D(X) + D(Y)
应用方差的定义:D(Z) = E{[Z-E(Z)]²} 和X,Y的独立性,
D(Z) = D(X+Y) = E{(X+Y)² - [E(X)+E(Y)² ]} = E[X² - E²(X)] + E[Y² - E²(Y)] +
+ E[2XY] - 2E(X) E(Y) = D(X) + D(Y) + 0
即: D(X+Y) = D(X) + D(Y)
温馨提示:答案为网友推荐,仅供参考