不忘初心 · 2023年12月17日
NO.PZ2020010302000008
问题如下：
What is E[XE[X]]?
Hint: recall that E[X] is a constant.
选项：
解释：
because E[X] is a constant and does not depend on X.
In other words, the expected value of a random variable does not depend on the random variable.
题干提示E(X)是常数，直接提到公式前面就可以了吧，E[XE(X)]=E(X)E(X)=E(X)^2，这样可以吗？为什么一定要答案那样的推导过程呢？
NO.PZ2020010302000008 问题如下 Whis E[XE[X]]? Hint: recall thE[X] is a constant. E[XE[X]]=ΣE[X]XPr(X=x)=E[X]ΣXPr(X=x)=E[X]∗E[X]=(E[X])2E[XE[X]] = ΣE[X]X Pr(X = x) = E[X]ΣX Pr(X = x)= E[X] * E[X] = (E[X])^2E[XE[X]]=ΣE[X]XPr(X=x)=E[X]ΣXPr(X=x)=E[X]∗E[X]=(E[X])2 because E[X] is a constant anes not penon X.In other wor, the expectevalue of a ranm variable es not penon the ranm variable. E[X] is a constant 这句话有没有影响结果么
NO.PZ2020010302000008 问题如下 Whis E[XE[X]]? Hint: recall thE[X] is a constant. E[XE[X]]=ΣE[X]XPr(X=x)=E[X]ΣXPr(X=x)=E[X]∗E[X]=(E[X])2E[XE[X]] = ΣE[X]X Pr(X = x) = E[X]ΣX Pr(X = x)= E[X] * E[X] = (E[X])^2E[XE[X]]=ΣE[X]XPr(X=x)=E[X]ΣXPr(X=x)=E[X]∗E[X]=(E[X])2 because E[X] is a constant anes not penon X.In other wor, the expectevalue of a ranm variable es not penon the ranm variable. In other wor, the expectevalue of a ranm variable es not penon the ranm variable.这句什么意思？和这道题什么关系?谢谢。
NO.PZ2020010302000008 E[XE[X]]=ΣE[X]XPr(X=x)=E[X]ΣXPr(X=x)=E[X]∗E[X]=(E[X])2 这个公式不是很懂，E[XE[X]] 为什么等于 ΣE[X]XPr(X=x)？ 谢谢
