Prove Jensen's Inequality: Var[X] ≥ (E[X])^2

[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.

 

[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.