# Question: Let X1 X2 X5 be a sequence of five independent

Let X1, X2… X5 be a sequence of five independent discrete random variables, each with a distribution described by:

(a) Find the probability mass function of the median (third largest) of these five samples. (b) For this random variable, is the median an unbiased estimate of the mean? That is, does the expected value of the median equal the mean of the Xi? Prove your answer.

(c) Find the variance of the median.

(a) Find the probability mass function of the median (third largest) of these five samples. (b) For this random variable, is the median an unbiased estimate of the mean? That is, does the expected value of the median equal the mean of the Xi? Prove your answer.

(c) Find the variance of the median.

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