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## Homework Statement

The random variables

*X*and

_{1}*X*are independent and identically distributed with common density

_{2}*f*for

_{X}(x) = e^{-x}*x*>0. Determine the distribution function for the random variable Y given by

*Y = X*.

_{1}+ X_{2}## Homework Equations

Not sure. Question is from Ch4 of the book, and convolutions for computing distributions of sums of random variables aren't introduced until Ch8.

Answer in the back of the book is

*F*for

_{Y}(y) = 1-e^{-y}(1+y)*y*>0.

## The Attempt at a Solution

Tried every convolution formula I could find (I found a bunch of different variations, and I'm not sure which ones are equivalent or correct): integral from zero to positive infinity of f(t)F(y-t)dt, F(t)f(y-t)dt, F(t)F(y-t)dt, and f(t)f(y-t)dt. All of them end up with a

*[tex]\int[/tex]e*, which gives me an infinity term.

^{t}e^{-t}Am I solving the integral wrong or not setting it up right or something else?