f(x)=a/b(x/b)^(a-1)exp(-(x/b)^a) for x>0.
i). find the cumulative distribution function F(x).I believe that i should start by antidifferentiation of f(x), but I was stuck there.
ii). calculate the n-th moment E(X^n) for all n=1,2,..Express it in terms of the Gamma function.
Making the substitution, we get :
But now, you gotta transform t^n with respect to y.
Hence the integral is :
Does it look clear ? Don't hesitate to tell if it is not.
I'm not that sure about the result, but I don't see where there would be a mistake ><