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.)

Type the correct answer in the box. consider the system of linear equations below. rewrite one of the two equations above in the form ax + by = c, where a, b, and c are constants, so that the sum of the new equation and the unchanged equation from the original system results in an equation in one variable.