Hi - Looking to see if there is a simple way to prove that if X1 is Cauchy(mu1, sigma1), and X2 is Cauchy(mu2,sigma2), X1 and X2 are indep, then X1+X2 is Cauchy with mu1+mu2 and sigmal1+sigma2.

Seems like a bear to go through the partial fraction decomp of the convolution density

Thanks much

Ravi