Thread: Density Function of U

I'm trying to solve this problem and am having trouble with the Y3 and Y4 concept. Previously I've only solved with Y1 and Y2. Any help is much appreciated!

Let Y1, Y2, Y3, Y4 be independent random variables with common density function:f(y) = e^-y, y>0 and 0, elsewhere. Let U = Y1 + Y2 + Y3 + Y4. Find the density function of U.

Hey bullmoose97.

Hint: If you have solved with Y1 and Y2, then do this again with (Y1 + Y2) + Y3 and then again for Y4. Also look at the MGF of a gamma distribution.