The joint probability distribution of variables X and Y is shown in the table below. ...............................................................................X..........................................................................

The joint probability distribution of variables X and Y is shown in the table below.

...............................................................................X.......................................................................

Y	1	2	3
1	0.30	0.18	0.12
2	0.15	0.09	0.06
3	0.05	0.03	0.02

Calculate E(XY)

Determine the marginal probability distributions of X and Y.

Calculate E(X) and E(Y)

Calculate V(X) and V(Y)

Are X and Y independent? Explain.

Find P(Y = 2| X = 1)

Calculate COV(X,Y). Did you expect this answer? Why?

Find the probability distribution of the random variable X + Y.

i. Calculate E(X + Y) directly by using the probability distribution of X + Y.

Calculate V(X + Y) directly by using the probability distribution of X + Y, and verify that V(X + Y) = V(X) + V(Y). Did you expect this result? Why?

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Expert Solution

orchestra answered 1 year ago

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