PaC Exercise 2.4

Exercise 2.4

Prove that E[X^k] ≥ E[X]^k for any even integer k ≥ 1.

Solution:

If k is even then so is k − 2. Therefore, the second derivative of the function f(x) = x^k is positive for all x and f is a convex function. The claim then follows by Jensen’s inequality.