1) Suppose that Y₁, Y2,...,Y₁ is a random sample from a population with probability densityfunction1,7,f(x)=B³Find the Maximum Likelihood Estimator of B.00elsewhere

Answered: 1) Suppose that Y₁, Y2,...,Y₁ is a…

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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For a statistic to be a good estimator of a parameter, two properties it must satisfy are unbiasedness and minimum variance. Consider a sample of three observations X₁, X₂, X, where X, ~ Exp (0). That is, a sample of size 3 is taken from a population 2 3 following the exponential distribution with density function given by f(x) = 1e % if x > 0 0, Otherwise. Five possible estimators of are â‚ =X₁, Ô₂ = ¹/(X₁ + X₂), Ô‚ = =— (X₁ + 2X₂), Ô¸ = X, and Ô¸ = ¹⁄ (X₂ + X). 2 [Hint: Use the fact that for variable X we have E(X)= 0 and E(X²)=20² and Var(X) = 0². (a) Show that the five estimators given above are unbiased for 0. (b) Find the variances of each of the five estimators. (c) Which estimator will you choose for 0. Why?
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1) Suppose that Y₁, Y2,...,Y₁ is a random sample from a population with probability density function 1,7, 00 elsewhere f(y)=B Find the Maximum Likelihood Estimator of B.