Question: Let ? and ? be jointly continuous RVs with a joint probability density function given as f X,Y (u,v) = c e -max(u,v) (0 <

Let ? and ? be jointly continuous RVs with a joint probability density function given as

fX,Y(u,v) = ce-max(u,v) (0 < u, v < ), otherwise 0

a. Find the constant c?.

b. Find the marginal pdfs of X and Y, i.e. fX(u) and fY(v)

c. What is P(X<2Y<4X)?

d. Let Z=X+Y be a new random variable. What are FZ(t) and fZ(t) for t>0?

e. Are X and Y independent? Provide a rigorous proof for your answer

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