please solve all the parts(a,b,and c).

Suppose $X$ and $Y$ are random variables with the given joint density function. $f (x, y) = {0.1 e^{? (0.5 x + 0.2 y)} 0 if x ? 0, y ? 0 otherwise$ (a) Is f a joint density function? (b) Find $P (r ? 8)$ . (Round your answer to four decimal places.) Find $P (X ? 3, Y ? 7)$ . (Round your answer to four decimal places.) (c) Find the expected value of $x$ . Find the expected value of $r$ .

Question

please solve all the parts(a,b,and c).
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Suppose

X

and

Y

are random variables with the given joint density function.

f (x, y) = {0.1 e^{? (0.5 x + 0.2 y)} 0 if x ? 0, y ? 0 otherwise

(a) Is f a joint density function? (b) Find

P (r ? 8)

. (Round your answer to four decimal places.) Find

P (X ? 3, Y ? 7)

. (Round your answer to four decimal places.) (c) Find the expected value of

x

. Find the expected value of

r

.

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(Solved): please solve all the parts(a,b,and c). Suppose X and Y are random variables with the given joint den ...