Can anyone help with how I'd program the below into Mathematica to get the solution?
Let Xi, i = 1, 2 be independent random variables (i.r.v.ís) having Gamma distribution with parameters (3, 1/2), i.e., Xi ~ Gamma(3, 1/2).
(i) Using characteristic functions and the inversion formula find the probability density function (pdf) of Y = X1 − X2.
(ii) Find also E(Y^4).
2) Do the same task for iid r.v.ís with the Cauchy distribution.