Question: B.2 Let X be a discrete random variable that is the value shown on a single roll of a fair die. (a) Represent the probability

B.2 Let X be a discrete random variable that is the value shown on a single roll of a fair die.

(a) Represent the probability density function f(x) in tabular form.

(b) What is the probability that X = 4? That X = 4 or X = 5?

(c) What is the expected value of X? Explain the meaning of E(X) in this case.

(d) Find the expected value of X2.

(e) Find the variance of X.

(f) Obtain a die. Roll it 20 times and record the values obtained. What is the average of the first 5 values? The first 10? What is the average of the 20 rolls?

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