Let (X,Y) be a random vector with joint PDF given by fX,Y(x, y) =(c ·(y/x)^4 if (x, y) ∈ R 0 otherwise) where c > 0 is an as-of-yet undetermined constant, and R is the region in the first quadrant below the graph of y = min{x, 1}. (a) Find the value of c that makes this a valid joint PDF. (b) Set up, but do not evaluate, the double integral corresponding to P(X + Y ≥ 2). (c) Find fX(x), the marginal PDF of X. (d) Find fY(y), the marginal PDF of Y. (e) Find E[X]. (f) Find E[Y].

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Let (X,Y) be a random vector with joint PDF given by fX,Y(x, y) =(c ·(y/x)^4 if (x, y) ∈ R 0 otherwise) where c > 0 is an as-of-yet undetermined constant, and R is the region in the first quadrant below the graph of y = min{x, 1}. (a) Find the value of c that makes this a valid joint PDF. (b) Set up, but do not evaluate, the double integral corresponding to P(X + Y ≥ 2). (c) Find fX(x), the marginal PDF of X. (d) Find fY(y), the marginal PDF of Y. (e) Find E[X]. (f) Find E[Y].

***For the first question 3a, To find the distribution of Y, you might want to calculate the c.d.f. first: F_{Y}(y) = P(Y <= y). Try to write the event Y <= y in terms of X so you can compute the probability.