Dear all

I have problem with the following question, i have solved one inequality like given below. Can anybody help me further for solving this problem

Let be a nonnegative even function that is non decreasing for positive x. Then for a random variable with ,

.

I tried like way.

Let be a random variable, then is non-negative

Consider,

Now since f is nondecreasing function

f is non-negative even, so

taking expectation, we get

Is this way is correct and can some one help me for second inequality.

Thanks in Advance.