The differentiation approach to derive the maximum likelihood estimator (mle) is not appropriate in all the cases. Let X₁, X2, X, be a random sample of size n from the population of X. Consider the probability function of X -{. [e-(2-0), if 0≤x<∞ for -∞ <<∞ otherwise. f(x;0)= (a) Argue that the mle of is the first order statistic (Y₁). Denote it by . (b) Find E(), and show that the mle of 0 is a biased estimator. (c) Derive the mean square error (mse) of 6.
The differentiation approach to derive the maximum likelihood estimator (mle) is not appropriate in all the cases. Let X₁, X2, X, be a random sample of size n from the population of X. Consider the probability function of X -{. [e-(2-0), if 0≤x<∞ for -∞ <<∞ otherwise. f(x;0)= (a) Argue that the mle of is the first order statistic (Y₁). Denote it by . (b) Find E(), and show that the mle of 0 is a biased estimator. (c) Derive the mean square error (mse) of 6.
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...
Related questions
Question
Transcribed Image Text:The differentiation approach to derive the maximum likelihood estimator (mle) is not
appropriate in all the cases. Let X₁, X2, Xn be a random sample of size n from the
population of X. Consider the probability function of X
f(x; 0) =
Je-(2-0), if 0<x<∞ for -x<<∞
0,
otherwise.
(a) Argue that the mle of is the first order statistic (Y₁). Denote it by 6.
(b) Find E(), and show that the mle of 0 is a biased estimator.
(c) Derive the mean square error (mse) of 6.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
