The document discusses joint continuous random variables x and y, providing a joint probability density function (p.d.f.) and instructions to find the p.d.f. of a new variable w defined as w = x + y. It asks for the application of the distribution function technique and identification of non-trivial regions for the p.d.f. Additionally, it includes a request to calculate the probability p(0 < w < 21).

1. 4. X and Y are joint continuous random variables and their joint p.d.f. is given by Let W be the
continuous random variable distributed by W = X + Y . (a) Find the p.d.f. of W using the
Distribution Function Technique. Be sure to determine where this p.d.f. is non-trivial. (10 pts.).
(b) Find P ( 0 < W < 2 1 ) ( 5 pts. )