Let X be a random variable such that |X|<=C (bounded). Let f be an even, non decreasing function over the positive values of x. Prove that:
[E(f(X))-f(a)]/f(C) <= P(|X-E(X)|>=a) <= [E(f(X-E(X))]/f(a).
The 2nd inequality is really easy to prove and it follows from chebyshev inequality...I am having hard time solving the first 1, any help is strongly appreciated. Thanks!
[E(f(X))-f(a)]/f(C) <= P(|X-E(X)|>=a) <= [E(f(X-E(X))]/f(a).
The 2nd inequality is really easy to prove and it follows from chebyshev inequality...I am having hard time solving the first 1, any help is strongly appreciated. Thanks!