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12 (10 points) Let X and Y have joint probability density function defined by f (X,Y) (x, y) = 1 2 x, if 0 < y < x < 2;• The probability of event {(X,Y)∈ B} is P(B)= X (x,y)∈B PX,Y (x,y) – Two coins, one fair, the other twoheaded A randomly chooses one and B takes the other X = ˆ 1 A gets head 0 A gets tail Y = ˆ 1 B gets head 0 B gets tail Find P(X ≥ Y) • Marginal probability mass function of X can be ob0, elsewhere Find the marginal probability density function of YYour answer should contain the region on which the marginal probability density function is nonzero 13 (10 points) Probability and CombinatoricsYou may leave your answer in terms of combinatorics symbols (n Test Set 6 Probability Density Function Correlation And Dependence What is joint probability density function