# Jensen's Inequality

1. Feb 14, 2005

### jetoso

The variance can be written as Var[X]=E[X^2]-(E[X])^2. Use this form to prove that the Var[X] is always non-negative, i.e., show that E[X^2]>=(E[X])^2.
Use Jensen's Inequality.

Any sugestions? I just tried to prove that a function g(t) is continuous and twice differentiable, such that g''(t) > 0 which must imply it is convex.
Then, I am stuck with the proof.

2. Feb 14, 2005

### mathman

I am not sure how to use Jensen's inequality. However by using the relationship:

E((X-E(X))2)=E(X2)-(E(X))2, the result is obvious.