I am a programmer and derived this formula for an algorithm I am working on.
R / ( R + X - Y)
Where R is a constant and X,Y are random variables from a LaPlace distribution. I wanted to know the expected value. Intuitively I thought it would be 1 because the expected value of X and Y are the same (the mean). However when I asked someone on a chat room they told me that
E[1/X] != 1/E[X]
I tried to calculate the expected value manually using the method explained in wiki i.e. integral from -inf to +inf of the formula multipled by the pdf. However this ended up in improper integrals and double integrals. Which I just looked up now. I don't think I have the skills to do this without making mistakes.
If anyone can help me it would be awesome. Thanks in advance