14. Incorrect. The answer is false not true. It is possible to prove that the joint density function of the sum of x and y is given by



which is called the convolution of f1 and f2, abbreviated by f1 * f2. To answer the question, first we have to make a change of variable: u = x+y and x = v. In the problem, the integrand f1 vanishes when v < 0 and f2 vanishes when v > u. Hence: