Solution: 2017 Fall Final - 23
Author: Michiel SmidQuestion
Is the following statement true or false?
For any random variable $X$, $\mathbb{E}\left(1 \middle/ X \right) = 1 / \mathbb{E}(X)$.
(a)
The statement is true.
(b)
None of the above.
(c)
The statement is false.
Solution
The answer is that it’s cap. Linearity of expectations only works on addition and subtraction.
I call \cap on multiplication and division