Two tire quality experts examine stacks of tires and assign quality ratings to each tire on a 3-point scare. Let X denote the grade given by experts A and let Y denote the grade given by B. the following table gives the joint distribution for X, Y.
Y
|
X |
1 |
2 |
3 |
|
1 |
0.10 |
0.05 |
0.02 |
|
2 |
0.10 |
0.35 |
0.05 |
|
3 |
0.03 |
0.10 |
0.20 |
i. Find P(X =1,Y = 3)
ii. Find P(X ? 2,Y ? 3)
iii. Find the marginal distribution of X
iv. Find the marginal distribution of Y
v. Find the conditional distribution of X |Y = 2
vi. Find P(X ?1|Y = 2)
vii. Calculate the correlation coefficient of X and Y.