Let x and y be independent exponential random variables with pa- rameter u > 0 and let z = x +y. (a) compute the density of z by using the convolution formula rtoo fz(z) = | fx (x) • fy(z – x) dx. -00 be precise on the domain for z and on the integration bounds for x in the above integral. (b) find the joint cumulative distribution function f(x, z)(x, z) of the random variables x and z. (c) find the joint density function f(x, z)(x, z) of x and z. hint: recall that əroz f(x, z)(x, z) = f(x, z)(x, z). (d) compute e[x|z = z]. 22