- #1

- 76

- 2

* X is a discrete random variable that is symmetrically distributed about 0. Hence, E(X) = 0

* Why is E(X^3) = 0 but E(X^2) is not necessarily zero?

* My intuition is that this is because X^3 and X are both odd functions. How would I write this out in equation form? Do I have to apply the law of total expectation (aka. law of iterated expectations)?

Any thoughts and suggestions would be appreciated. Thank you!