1. Suppose we have a random sample X₁, X2, ..., Xn from an Exponential distribution with mean1/A. Suppose we want to estimate the mean 1/A. One estimator for 1/X is T₁ = X. Of interestis to note that the minimum of X₁, X2,..., Xn, say X(1), has an Exponential distribution withmean (n)-¹.(a) Show that T₁ is an unbiased estimator of 1/A.(b) Find the constant a such that T₂ = aX(1) is an unbiased estimator of 1/X.(c) Since T₁ and T₂ are both unbiased we prefer the estimator with smaller variance. Whichof the estimators T₁ and T₂ would you choose for estimating the mean 1/X?

Given that X1, X2, .....Xn follows Exponential with mean 1/λ, then Variance of X is = Var(X) = 1/λ2…

Answered: (a) Show that T₁ is an unbiased…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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