Two convicts are running away from prison. One man, John, runs east X miles, and another man, Jeff, runs north Y miles. John cannot run more than 4 miles, and Jeff cannot run more than 6 miles. At a random point in time, their locations are spotted by a helicopter. Assume that the joint density of their location is
fX,Y (x,y) = 1/24,
for 0 ≤ x ≤ 6, and 0 ≤ y ≤ 4
and fX,Y(x,y) = 0 otherwise. Let g{x,y) = x + y be the total distance that the two men have run so far.
a. Find the expected value of the sum of these two distances.
b. Find the variance of the sum of these two distances.