PLEASE DONT COPY ANSWERS FROM ANY OTHER SOURCES.ONLY CORRECT ANSWERS PLEASE! PLEASE DONT ANSWER IF YOU ARE NOT AWARE OF IT. 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?

It is given that X1, X2, ....Xn follows Exponential with mean 1/λ then the variance of X is 1/λ2…

(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. Which of the estimators T₁ and T₂ would you choose for estimating the mean 1/X?