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(i) Let X,.... X, and Y,..... Y, be independent random samples, respectively, from the N(H,, )-and the N(H2, r²)- distributions. Here the parameters a,. , and cr' are all unknown. Explain carefully how you would test the hypothesis H,: H,=H2 against H: µ,#H,. (ii) Let X..... X, be a random sample from the distribution with the PDF S(x; 0) =e--), for 0

(i) Let X,.... X, and Y,..... Y, be independent random samples, respectively, from the N(H,, )-and the N(H2, r²)- distributions. Here the parameters a,. , and cr' are all unknown. Explain carefully how you would test the hypothesis H,: H,=H2 against H: µ,#H,. (ii) Let X..... X, be a random sample from the distribution with the PDF S(x; 0) =e--), for 0

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(i) Let X,..... X, and Y,. .... Y, be independent random samples, respectively, from the N(H,, ²)-and the N(H2, r²)- distributions. Here the parameters u. #, and er are all unknown. Explain carefully how you would test the hypothesis H,: H, =H2 against H,: µ, #µ,. (ii) Let X. . X, be a random sample from the distribution with the PDF S(x: 0) =e-(-0), for 0<x< o, where 0 has a prior distribution the standard normal N(0, 1). Determine the posterior distribution of 0. Suppose that 0 is to be estimated when the loss function is the absolute error loss, L(a, 0) = |a – 0|. Determine the optimal Bayes estimator and express it in terms of the function c,(x) defined by 20(c,(x) – n) =Þ(x-n), for - 00 <x< 00, where is the standard normal distribution function.
Transcribed Image Text:(i) Let X,..... X, and Y,. .... Y, be independent random samples, respectively, from the N(H,, ²)-and the N(H2, r²)- distributions. Here the parameters u. #, and er are all unknown. Explain carefully how you would test the hypothesis H,: H, =H2 against H,: µ, #µ,. (ii) Let X. . X, be a random sample from the distribution with the PDF S(x: 0) =e-(-0), for 0<x< o, where 0 has a prior distribution the standard normal N(0, 1). Determine the posterior distribution of 0. Suppose that 0 is to be estimated when the loss function is the absolute error loss, L(a, 0) = |a – 0|. Determine the optimal Bayes estimator and express it in terms of the function c,(x) defined by 20(c,(x) – n) =Þ(x-n), for - 00 <x< 00, where is the standard normal distribution function.
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