I was not able to decide the limits of the integrals while calculating pdf in following question:
Consider two independent random variables X and Y. Let fX(x) = 1 − x/2
if 0 < x < 2 and 0 otherwise. Let fY (y) = 2 − 2y for 0 < y < 1 and 0
otherwise. Find the probability density function of X + Y.