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
	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)