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Suppose that a random variable X always takes one of the integer values 1, 2, 3 , 4, or 5. The probability function for X is given by: Pr(Xi) =Xi/15.

a. What is the population mean (μ) for this random variable?

b. Suppose you did not know Pr(Xi) but could observe random samples of values of X. You could then use these samples to calculate X(the sample mean). Explain the sense which X calculated in this way is a random variable.

c. X is a random variable, so it has an expected value. What is E(X)?

d. Is the following statement true or false? X is an unbiased estimator ofμ, so X will always equal to μ.

Explain your answer

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