I'm faced with the following problem: I have to lower bound the expected value of the n-th root of an arbitrary distributed real random variable using its expected value. So I'm looking for something that has a similar form as the Jensen inequalty but goes the other way around.
I can assume the variable satisfies 0< X< 2 so I thought I could lower bound the root by a line but that approximation is to strong.
Does any one know a way of lower bounding the expected value of a root?