Question

1. The joint prob dist of X and Y is given by:

P(x,y)=K|x-y|, x=0,1,2, y = 1, 2, 3, 4

a) Determine the value of K.

b) Determine the marginal distribution of X and hence compute E(X) and

Var(X).

c) Determine the marginal distribution of Y and hence compute E(Y) and

Var(Y).

d) Determine E(X|y=3) and Var(Y|y=3).

e) Are X and Y independent?

2. The joint prob dist of X and Y is given by:

P(x,y) = Kxy, x=1,2,3, 4 and y less than or equal to x.

a) Determine the value of K.

b) Determine the conditional distribution of X, given Y = 3. Hence compute

E(X|y=3) and Var(X}y=3).

c) Are X and Y independent?

3. The joint prob dist of X and Y is given by:

P(X=a,Y=a) = p_{11}, P(X=a, Y=b) = p_{12}, P(X=b, Y=a)=p_{21} and

P(X=b,Y=b)=p_{22}.

Compute the correlation between X and Y and state the condition under

which X and Y will be uncorrelated. Verify that this condition also

implies independence of X and Y.

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Answer 1