**14. Correct. The answer is false. **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* f*_{1} and *f*_{2}, abbreviated by *f*_{1
}* f_{2}. To answer the question, first we have to make a
change of variable: *u = x+y* and *x = v*.
In the problem, the integrand *f*_{1}
vanishes when *v* < 0 and *f*_{2} vanishes when *v > u*. Hence: