# Question

Suppose Xm, m = 1, 2,….,n are a sequence of independent and exponentially distributed random variables with

Assuming that is an odd number (n = 2k –1 for some integer ):

(a) Find the PDF of the median of the sequence.

(b) Find the expected value of the median of the sequence. Is the median an unbiased estimate of the mean of the underlying exponential distribution?

(c) Find the variance of the median of the sequence.

Assuming that is an odd number (n = 2k –1 for some integer ):

(a) Find the PDF of the median of the sequence.

(b) Find the expected value of the median of the sequence. Is the median an unbiased estimate of the mean of the underlying exponential distribution?

(c) Find the variance of the median of the sequence.

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