Let X1, , X21 be i i d with the exponential distribution that has parameter 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 distribution of the Xis a Determine the median of the distribution of X1 b Let be the M S E of the sample median when 1 Prove that the M S E of the sample median equals 2 in general c Describe a simulation method for estimating

Question: Let X1, . . . , X21 be i.i.d. with the exponential distribution that has parameter . Let M stand for the sample median. We

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.

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a The cdf of each X i is Fx 1 expx for x 0 The median is log2 b ... View full answer

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