Hi, I'm trying to derive the moment generating function for the Rayleigh distribution.
I know that it equals E(e^(t*x)), which is the following integral that can be seen here, evaluated at the limits of 0 and infinity:
Where the parameter is σ.
However, I'm having trouble in the actual derivation of this. I've been trying to do a change of variable where u = -(x^2/(2*(sigma^2))), so that I can get the integral to appear somewhere for the error function, but I'm not making any progress. Can someone help me in moving this along? Thanks.