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
The characteristic function of the distribution of the sum of independent RVs is the product of their characteristic functions. Look up the CF of the Cauchy distributions multiply them and you will find that it is of the same form as a Cauchy distribution with the required properties.
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