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.