Let X~ Exp(\), an exponential distribution with parameter > 0. This is a continuousprobability distribution on the non-negative real numbers, with p.d.f. given by2fx(t) = Xe-Allt>0ле1t≥0.(i) Verify (by calculation) that the log-likelihood function for the parameter A is given byl(x; λ) = n(log λ - Xã).(ii) Derive the MLE estimator for λ, and use it to compute the MLE estimate for thefollowing sample data ³: 1.1 5.5 0.6 1.3 0.5 2.1 4.6 4.6 0.8 3.9 3.7 0.8 0.9 0.8(iii) What is the MLE estimator for 1/λ? Verify this estimator is unbiased.

It is given that X follows Exponential distribution with given pdf.

Answered: ле t>0. (i) Verify (by calculation)…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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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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ле t>0. (i) Verify (by calculation) that the log-likelihood function for the parameter X is given by l(ể; \) = n(log } – A). - (ii) Derive the MLE estimator for λ, and use it to compute the MLE estimate for the following sample data ³: