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.)

a)its a joint function

b.)

Step-by-step explanation:

check the attachment for solutions

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.