Is it always true that E[X2]≥(E[X])2 ?
Yes or No
No, it is not always true that E[X^2] ≥ (E[X])^2.
The statement mentioned is an inequality known as the "Jensen's inequality." It applies to convex functions, which means that the function must satisfy certain conditions. In this case, the function X^2 is a convex function.
Jensen's inequality states that for a random variable X and a convex function g, we have:
E[g(X)] ≥ g(E[X])
If we have a convex function g(x) = x^2, then the inequality becomes:
E[X^2] ≥ (E[X])^2
However, if X is a non-convex function or if the conditions for Jensen's inequality are not met, then this inequality does not hold. So, in general, it is not always true that E[X^2] ≥ (E[X])^2.