Question: 8. Let X be a random variable with mean 6 and variance 3. Let Y be the random variable counting the number of times the

8. Let X be a random variable with mean 6 and variance 3. Let Y be the random variable counting the number of times the number 1 appears when rolling six fair four-sided dice. Assume that X and Y are independent. Define Z to be the random variable 2X - 3Y + 1. Find E(Z). 9. Suppose that the distribution of X is in the form f(x) = Cr for r in the interval [-1, 2]. (a) Determine the constant C which makes f a pdf. (b) Find the cumulative distribution function F(z). (c) Calculate the probability P(1

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