1. Discrete Random Variable Eagle Spice Company found that 75% of crab house restaurants in Maryland use their Old Chesapeake Bay Seasoning to steam blue crabs. Suppose that a random sample of five crab house restaurants is selected. Let the random variable X denote the number of crab house restaurants in the sample that use Old Chesapeake Bay Seasoning to steam crabs.

Construct the probability distribution of X assuming that independence holds.

a. Find the expected value of X.

b. Find the variance of X.

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2. Bivariate Probability Distribution The bivariate probability distribution of X and Y is given in the table below.

y x 4 5 6 1 .25 .10 .05 2 .15 .05 .15 3 .05 .15 .05

a. Obtain the marginal probability distribution of Y.

b. Obtain the conditional probability distribution of X when Y = 4.

c. Obtain the conditional probability distribution of Y when X = 2.

d. Are X and Y independent? Explain.

e. Calculate Cov(X,Y).