Determining marginal probability distributions

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Reference no: EM1316798

Q1) Joint probability distribution of variables X and Y is illustrated in table below, where X is number of tennis racquets and Y is number of golf clubs sold daily in small sports store.

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

a) Compute E(XY)

b) Determine marginal probability distributions of X and Y.

c) Are X and Y independent? Explain.

d) Compute conditional probability P(Y = 2 | X = 1)

e) Compute expected values of X and Y.

f) Compute variances of X and Y.

g) Compute Cov(X,Y). Did you expect this answer? Explain why?

h) Determine the probability distribution of random variable X + Y.

i) Compute E(X + Y) and Var(X + Y) directly using probability distribution of X + Y .

j) Illustrate that Var(X + Y) = Var(X) + Var(Y). Did you expect this result? Describe why?

Reference no: EM1316798

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