3) The joint probability distribution of variables X and Y is shown in the table below,...

 

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3) The joint probability distribution of variables X and Y is shown in the table below, where X is the number of tennis racquets and Y is the number of golf clubs sold daily in a small sports store. Tennis racquets (X) 1 2 3 Golf 1 0.30 0.18 0.12 Clubs 2 (Y) 0.15 0.09 0.06 3 0.05 0.03 0.02 a) Calculate the expected values of X and Y. E(X) = 1.7 E(Y) = 1.5 b) Calculate the variances of X and Y Var(X) = .61 Var(Y) = .45 c) Calculate the conditional probability P(Y= 2|X= 1). 0.3 d) Calculate Cov(X,Y). -0.2 3) The joint probability distribution of variables X and Y is shown in the table below, where X is the number of tennis racquets and Y is the number of golf clubs sold daily in a small sports store. Tennis racquets (X) 1 2 3 Golf 1 0.30 0.18 0.12 Clubs 2 (Y) 0.15 0.09 0.06 3 0.05 0.03 0.02 a) Calculate the expected values of X and Y. E(X) = 1.7 E(Y) = 1.5 b) Calculate the variances of X and Y Var(X) = .61 Var(Y) = .45 c) Calculate the conditional probability P(Y= 2|X= 1). 0.3 d) Calculate Cov(X,Y). -0.2