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Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0...

Question

Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0...

Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0 s S1 and 0 sy< 2 and f(x,y) elsewhere. a. Compute P(X+Y2 1). b. What is the probability that (X, Y) E A where A is the region bounded above by the parabola y 2 c. What is the probability that both X, Y exceeding 0.5? d. What is the probability X will take on values that are at least 0.2 units less than Y e. Compute the covariance of X,Y f. Compute the expected value X given that Y >1 g. Compute the expected value of min(X, Y) g. What is probability that X, Y are within 0.1 of each other?

Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0 s S1 and 0 sy< 2 and f(x,y) elsewhere. a. Compute P(X+Y2 1). b. What is the probability that (X, Y) E A where A is the region bounded above by the parabola y 2 c. What is the probability that both X, Y exceeding 0.5? d. What is the probability X will take on values that are at least 0.2 units less than Y e. Compute the covariance of X,Y f. Compute the expected value X given that Y >1 g. Compute the expected value of min(X, Y) g. What is probability that X, Y are within 0.1 of each other?

Answers

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