View Single Post
glacier302
#1
Feb15-12, 04:47 AM
P: 37
1. The problem statement, all variables and given/known data

Let X and Y be independent random variables each having the Cauchy density function f(x)=1/(∏(1+x2)), and let Z = X+Y. Show that Z also has a Cauchy density function.

2. Relevant equations

Density function for X and Y is f(x)=1/(∏(1+x2)) .
Convolution integral = ∫f(x)f(y-x)dx .

3. The attempt at a solution

My book gives the following hint, saying to "check it":

f(x)f(y-x) = (f(x)+f(y-x))/(∏(4+y2)) + 2/(∏y(4+y2))(xf(x)+(y-x)f(y-x)) .

Using this hint, I'm able to solve the rest of the problem, but I can't figure out how to prove that this hint is true.

Any help would be much appreciated : )
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds