Let X1, . . . , X21 be i.i.d. with the exponential distribution that has parameter .

Question:

Let X1, . . . , X21 be i.i.d. with the exponential that has parameter λ. Let M stand for the sample median. We wish to compute the M.S.E. of M as an estimator of the median of the of the Xi’s.
a. Determine the median of the of X1.
b. Let θ be the M.S.E. of the sample median when λ = 1. Prove that the M.S.E. of the sample median equals θ/λ2 in general.
c. Describe a simulation method for estimating θ.
Distribution
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