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The joint probability distribution of variables X and Y is shown in the table below, where X is the number of tennis racquets and Y is the number of golf clubs sold daily in a 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. a.      find out E(XY 

b. Find out the marginal probability distributions of X and Y.

c. Are X and independent? Describe.

d. Compute the conditional probability P(= 2 | = 1)

e. Compute the expected values of X and Y.

f. Compute the variances of X and Y. 

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

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

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

j. Show that Var(X + Y) = Var(X) + Var(Y). Did you expect this result?  Why?

Statistics and Probability, Statistics

  • Category:- Statistics and Probability
  • Reference No.:- M920556

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