Solution: 2022 Winter Final - 23
Author: Michiel SmidQuestion
Is the following statement true or false?
For any random variable $X$, $\mathbb{E}(X^2) = \mathbb{E}(X)\cdot \mathbb{E}(X)$.
(a)
The statement is false
(b)
The statement is true
(c)
The statement is neither true nor false
Solution
No, what you’re talking about is linearity of expectations, which only works for sums and differences, not products and quotients
Thus, the statement is false