Let the probability density of random variable (x, y) be f (x, y) = e ^ - (x + y), x > = 0, Y > = 0, and find the probability density function of Z = 1 / 2 (x + y) Using the distribution function to find the,

Let the probability density of random variable (x, y) be f (x, y) = e ^ - (x + y), x > = 0, Y > = 0, and find the probability density function of Z = 1 / 2 (x + y) Using the distribution function to find the,

I calculate - 2E ^ (- 4Z) + 2E ^ (- 2Z) is the integral of F (x, y) under x + y ≤ 2Z and then the differential. I don't know if there is any mistake. We can discuss it~