Question: Random variables X and Y depend on a single spin of two ordinary six-sided dice. Each has six faces (with one to six dots), and

Random variables X and Y depend on a single spin of two ordinary six-sided dice. Each has six faces (with one to six dots), and the dice are fair (each outcome is equally likely).

Random variable X is the three times the difference between the two outcomes. The difference is the maximum number rolled minus the minimum number rolled. (So, if the dice results are two 1's, the value of X is zero; if the dice results are a 1 and a 2, the value of X is 3, and so on.

Random variable Y is the product of the two outcomes. So, if the dice results are two 1's, the value of Y is one; if the dice results are a 2 and a 4, the value of Y is 8, and so on.

a. Calculate the expected value of X.

b. Calculate the expected value of Y.

c. Calculate the standard deviation of X.

d. Calculate the standard deviation of Y.

e. Calculate covariance between X and Y.

f. Calculate correlation between X and Y

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