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乘积的期望

Expected value of product

专题
Probability / 概率
难度
L2

题目详情

XX 为公平六面骰点数，YY 为独立的公平八面骰点数。求 E(XY)E(XY)。

XX is a fair 6-sided roll, YY is an independent fair 8-sided roll. Find E(XY)E(XY).

解析

由于独立：

E(XY)=E(X)E(Y).E(XY)=E(X)E(Y).

六面骰 E(X)=3.5E(X)=3.5，八面骰 E(Y)=4.5E(Y)=4.5，所以

E(XY)=3.5×4.5=15.75.E(XY)=3.5\times 4.5=15.75.

Original Explanation

Because they’re independent:
E(XY)=E(X) E(Y).E(XY) = E(X)\,E(Y). For a 6-sided die, E(X)=3.5.E(X)=3.5. For an 8-sided, E(Y)=4.5.E(Y)=4.5. So
E(XY)=3.5×4.5=15.75.E(XY) = 3.5 \times 4.5 = 15.75.