Determine conditional probability distribution

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Reference no: EM1316583

Determine Conditional probability distribution.

Suppose that during a basketball practice. Joe tries 3 shots from the free throw line; imagine further that he has a probability equal to 0.6 of making each shot and that the attempts are independent. Let 'X' be the number of baskets he makes in the first two shots and let Y be the number of baskets he makes in the last two shots. The marginal density for X and Y are each binomial with n = 2 and p = 0.6. The following 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

Note that the probability values for the events {2. 0} and {0. 2} are not defined and hence each is assigned to be equal to zero for this problem.

a) Complete the table showing joint distribution function for X and Y for this problem using information shown in the table above

Y	X
Y	0	1	2
0
1
2

b) Determine the marginal densities of X and Y

c) Find out the conditional probability f (X | Y= l) and hence compute P(X = 0 | Y = l)

d) Find out the conditional probability f (X = 2 | Y) and hence compute P(X = 21 Y = 0)

Reference no: EM1316583

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