- #1
slakedlime
- 76
- 2
This is not a homework problem but is rather something I'm curious about. I apologize if the answer is very simple, but I am having trouble coming up with an absolute and strict proof.
* 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!
* 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!