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

f_X,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. f_X(u) and f_Y(v)

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

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

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