Two 6-sided dice are rolled and the two resulting values X and Y are multiplied together to form the quantity Z = X · Y . Also, denote the average value of X and Y as Z′ = (X+Y)/2 (a) What are the expected value and the variance of the random variable Z? [Hint: Use the independence of the two separate dice.] (b) What are the expected value and the variance of the random variable Z′ ?

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