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
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)