Hello, Actex recently posted a really good challenge problem on their facebook page, and I've been trying to figure it out thus far, which eventually turned into deriving the variance of Pareto Distribution. The PDF is
f(x)= (a(n^a))/((x+n)^(a+1)) for x>0, a>0, n>0.
So I've been able to calculate E[x], because I'm going to have to square it in the end anyways, and got
E[x] = n/(1-a)
However I'm having trouble computing the integral for E[x^2], the second movement of the distribution.
Could anyone at least give me some sort of hint on it? I know partial fraction decomp won't work because we have a power of a..I've been thinking maybe trig sub as well, however I'm not entirely sure.
If you aren't particularly up on probability, computing E[x^2] is the same as computing(for this problem) the integral from 0 to infinity of (x^2)f(x) dx