Question

2. Suppose that X and Y have a discrete joint distribution for which the joint p.f. is defined as follows: cly - xfor x = -3,

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Answer #1

For a valid probability distribution sum of probabilities must be equal to 1. Following table shows the calculations:

X Y |Y-X| c|Y-X|
-3 -2 1 1c
-3 -1 2 2c
-3 0 3 3c
-3 1 4 4c
-1 -2 1 1c
-1 -1 0 0
-1 0 1 1c
-1 1 2 2c
1 -2 3 3c
1 -1 2 2c
1 0 1 1c
1 1 0 0
2 -2 4 4c
2 -1 3 3c
2 0 2 2c
2 1 1 1c
Total 30c

For a valid probability distribution 30c must be equal to 1 so

30c = 1

c = 1/30

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Following are the set of values for which X <= Y :

X Y |Y-X| c|Y-X|
-3 -2 1 1c
-3 -1 2 2c
-3 0 3 3c
-3 1 4 4c
-1 -1 0 0
-1 0 1 1c
-1 1 2 2c
1 1 0 0
Total 13c

Therefore,

13 P(XY) 13c 0.4333 30

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