Consider two continuous random variables X and Y whose joint den- sity is defined by fx.y...

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Consider two continuous random variables X and Y whose joint den- sity is defined by fx.y (r,y) cry + whenever 0 < 2,y < 1, and fxy(r, y) = 0, otherwise. (a) Determine the value of the real-valued constant c. (b) Determine the (marginal) density functions of X and Y. (c) Determine the joint distribution function of X and Y. (d) Determine the probabilities P(X <,Y < ) and P(X <Y). (e) Are X and Y independent? Consider two continuous random variables X and Y whose joint den- sity is defined by fx.y (r,y) cry + whenever 0 < 2,y < 1, and fxy(r, y) = 0, otherwise. (a) Determine the value of the real-valued constant c. (b) Determine the (marginal) density functions of X and Y. (c) Determine the joint distribution function of X and Y. (d) Determine the probabilities P(X <,Y < ) and P(X <Y). (e) Are X and Y independent?