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## Statistics

describe conditional probability distribution.

Presume that during a basketball practice. Joe tries three shots from the free throw line, presume further that he has a probability equal to 0.6 of making each shot as well as that the attempts are independent. Let X be the number of baskets he makes in the first two shots also let Y be the number of baskets he makes in the last two shots. The marginal density for X as well as Y are each binomial with n = 2 and p = 0.6. The subsequent table shows the assignment of the probabilities.

 Outcome HHH HHM HMH HMM MHH MHM MMH MMM Probability (0.6)3 (0.6)2 (0.4) (0.6)2(0.4) (0.6) (0.4)2 (0.6)2(0.4) (06) (0.4)2 (06) (0.4)2 (0.4)3 Value for X 2 2 1 1 1 1 0 0 Value for Y 2 1 1 0 2 1 1 0

Please note that the probability values for the events {2. 0} and {0. 2} aren't defined and hence each is assigned to be equal to zero for this problem.

1) Complete the table showing the joint distribution function for X as well as Y for this problem using information shown in the table above

 Y X 0 1 2 0 1 2

2) Define the marginal densities of X and Y

3) Define the conditional probability f (X | Y= l) and hence compute P(X = 0 | Y = l)

4) Define the conditional probability f (X = 2 | Y) and hence compute P(X = 21 Y = 0)

Statistics and Probability, Statistics

• Category:- Statistics and Probability
• Reference No.:- M920241

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