Suppose X and Y are random variables with joint density function.

f(x, y) = 0.1e−(0.5x + 0.2y) if x ≥ 0, y ≥ 0
f(x, y) = 0 otherwise

(a) Is f a joint density function?
(b) Find P(Y ≥ 8). (Round your answer to four decimal places.) Find P(X ≤ 7, Y ≤ 2). (Round your answer to four decimal places.)