Question

Prove that if E(X) = 0, then V(X) = E(X² ).

Answer 1

Given E(X) = 0. To show V(X) = E (X² ) 

We know that Var (X) = E(X² ) – [E(X)]² 

So if E(X) = 0, Var (X) = E(X² ) 

From the definition of the variance of X also we can see the result.

Var(X) = Σ[x – E(x)]² p(x) 

If E (X) = 0, then V(X) = Σ x² p(x) = E(X²)