The Expectation of X and the Expectation of X squared (discrete math)

[SammC]

Homework Statement

prove or disprove that E[X^2] = E(X)^2

Homework Equations

E[X] = $$\sum$$x_i*pr(x_i)

The Attempt at a Solution

I really don't know where to start, I believe that it is not true, so I should try to disprove it, and the easiest way to do that would be by counterexample... I don't understand expectation very well though, I could try to do a mathematical proof to show that they are not equal, but I don't know how to go about that either.

 

[lanedance]

hi sammC - this is ripe for a counter example...

easiest would be to try a distribution with only 2 outcomes, ie 50% probability of each occurring, then calculate E[x] and E[X^2]

note E[X^2] = sum over i of pr(xi)*(xi^2)

 

[SammC]

ah, this helps a bunch, thanks!