Bootstrapping the distribution and the SE of the median of exponentially distributed random variables. (a) Show...

 

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Bootstrapping the distribution and the SE of the median of exponentially distributed random variables. (a) Show that the median of the Exp(X) distribution is mx = (log 2)/λ. (Hint: Check Week 4 Lectures, Part 1.) 2 (b) Consider a random sample X₁, Xn from Exp(X). Denote the sample median of the random sample by Med(X₁,..., Xn). Suppose that we estimate A by 1/Xn. De- scribe the parametric bootstrap procedure to estimate the distribution and the SE of Med(X₁,... Xn) — mx. Bootstrapping the distribution and the SE of the median of exponentially distributed random variables. (a) Show that the median of the Exp(X) distribution is mx = (log 2)/λ. (Hint: Check Week 4 Lectures, Part 1.) 2 (b) Consider a random sample X₁, Xn from Exp(X). Denote the sample median of the random sample by Med(X₁,..., Xn). Suppose that we estimate A by 1/Xn. De- scribe the parametric bootstrap procedure to estimate the distribution and the SE of Med(X₁,... Xn) — mx.

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Solution 2 a Fx x 1 exp2x median is m sot Fx m 05 1 exp 2m 05 Log 2 ... View the full answer