Question

GIVEN INFORMATION

{X=0, Y=0} = 36 {X=0, Y=1} = 4 {X=1, Y=0} = 4 {X=1, Y=1} = 6

1. Use observed cell counts found in the given information to estimate the joint probabilities for (X = x, Y = y)

2. Find the marginal probabilities of X = x and Y = y

3. Find P (Y = 1|X = 1) and P (Y = 1|X = 0)

4. Find P (X = 1 ∪ Y = 1)

5. Use the estimated marginal probabilities found in part 2 above to compute E(X), E(Y ), Var(X), and Var(Y ). Do these agree (at least approximately) with the sample average and sample variance of X and Y?

6. Use the estimated joint probabilities found in part 2 above to compute Cov(X, Y ).

7. Are X and Y independent? Explain.

Answer 1

Solution:

(7) No, X and Y are not independent, because P(X = x, Y = y) P(X = x) * P(Y = y) for x = 0,1 and y = 0,1).

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