Just C please 2. Suppose that X₁,..., Xn form a random sample from a Exponential(\) distribution, with PDFgiven byf(x|λ) = Ae¯λx for x > 0, λ > 0.In the above form, À is a rate parameter and E(X) = 1/λ and var(X) = 1/λ².(a) Find a MOM (method of moment) estimator Ã of X.(b) Write down the likelihood function Ln (A) and obtain the maximum likelihood estimator(MLE) Â of A.(c) Let 7 denote the population median. Obtain the MLE of T. (Hint: First find the specificform of the median in terms of λ and utilize the invariance property of MLE)(d) Is it easy to study the finite-sample distributional property of the MLE Â, such as E(Â),var(Â), the mean square error (MSE) in estimating \, and its exact sampling distribution?(e) Compute the Fisher information In in the sample data. Accordingly, obtain the asymp-totic distribution of Â.(f) Obtain a sufficient statistic T(X₁,..., X₂) for À via the factorization theorem. Verify thatthe MLE Â is a function of T.

Answered: Image /qna-images/answer/3961c552-bbb5-45c5-a7a9-5dbc5f554fc8.jpg

Answered: (c) Let 7 denote the population median.…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(c) Let 7 denote the population median. Obtain the MLE of T. (Hint: First find the specific form of the median in terms of A and utilize the invariance property of MLE) (d) Is it easy to study the finite-sample distributional property of the MLE Â. such as E(X).