Police cars are randomly stationed throughout the town. When an emergency occurs, the distance a police car must travel north or south is a random variable X with density
fX(x) = 1/6
for 0 ≤ x ≤ 6,
and fX{x) = 0 otherwise. The distance a police car must travel east or west is a random variable Y with density
fY(y) = 1/6
for 0 ≤ y ≤ 6,
and fY(y) = 0 otherwise. Assume that X and Y are independent. So X + Y is the total distance traveled. Find the probability that X + Y ≤ 4.
(First find the joint density fX,Y(xi V) °f x and Y", and draw a picture for where the joint density is defined. If you write an integral for the probability, the integrand is constant. So you can compute the desired area in your picture, divided by the total area.)