a) Y can take the values as 1, 2, 3, 4, 6, 9
| Y | ![]() |
![]() |
| 1 | (1,1) | ![]() |
| 2 | (1,2) , (2,1) | ![]() |
| 3 | (1,3) , (3,1) | ![]() |
| 4 | (2,2) | ![]() |
| 6 | (2,3) , (3,2) | ![]() |
| 9 | (3,3) | ![]() |
So the PMF is
| Y | 1 | 2 | 3 | 4 | 6 | 9 |
| P(y) | 1/36 | 1/9 | 1/6 | 1/9 | 1/3 | 1/4 |
b) Z can take the values as
The values with the corresponding probabilities are
| Z | ![]() |
P(z) |
![]() |
(1,3) | ![]() |
![]() |
(1,2) | ![]() |
![]() |
(2,3) | ![]() |
![]() |
(1,1), (2,2), (3,3) | ![]() |
![]() |
(3,2) | ![]() |
![]() |
(2,1) | ![]() |
| 3 | (3,1) | ![]() |
So the probability distribution is
| Z | ![]() |
![]() |
![]() |
1 | ![]() |
2 | 3 |
| P(z) | 1/12 | 1/18 | 1/6 | 7/18 | 1/6 | 1/18 | 1/12 |
The joint probability distribution for Xi and X2 is T1T2 f (1, 2)L22 for 1 1,2,3...
5. Suppose that three random variables Xi, X2, and X3 have a continuous joint distribution with the following p.d.f. (x1+2x2+3z3) and f(1, r2, 3) 0 otherwise. (a) Determine the value of the constant c; (b) Find the marginal joint p.d.f. of Xi and X3; (c) Find P(Xi < 1|X2-2, X3-1)
anwer this ..The answer must be??
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