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
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.