# Thread: evaluate expected value (normal distribution)

1. ## evaluate expected value (normal distribution)

I have to evaluate the expectation of the following function and no clue how to do it.

E ( (x-k)^{-gamma}), where gamma is a positive integer larger than 1, k is a constant and x follows a normal distribution N(mu, simga^2).
(1) Is it possible to find an expression for this expectation?
(2) What is this expression (maybe with restrictions on gamma)? Is it obtained with the help of integration by parts?

Thanks a lot!

2. Originally Posted by jazz123
I have to evaluate the expectation of the following function and no clue how to do it.

E ( (x-k)^{-gamma}), where gamma is a positive integer larger than 1, k is a constant and x follows a normal distribution N(mu, simga^2).
(1) Is it possible to find an expression for this expectation?
(2) What is this expression (maybe with restrictions on gamma)? Is it obtained with the help of integration by parts?

Thanks a lot!
Do you know how to at least set up the integral?

3. I set it up like this:
Int (x-k)^{-gamma} f(x) dx
where the integral goes from - infinity to + infinity and f(x) is the pdf of the normal distribution. Is it this what you mean?

4. Originally Posted by jazz123
I set it up like this:
Int (x-k)^{-gamma} f(x) dx
where the integral goes from - infinity to + infinity and f(x) is the pdf of the normal distribution. Is it this what you mean?
Yes. So what have you tried?

5. Well, this is where I am lost. I have don't know how to continue. Do you have an idea?