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1) Suppose that Y₁, Y2, function Y is a random sample from a population with probability density www 1 1-8 f(y) [By 0. Find the Maximum Likelihood Estimator of B. 00 elsewhere

1) Suppose that Y₁, Y2, function Y is a random sample from a population with probability density www 1 1-8 f(y) [By 0. Find the Maximum Likelihood Estimator of B. 00 elsewhere

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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ter Font Paragraph eatures are disabled because your Office product is inactive. To use for free, sign in and use the Web version. Activate 2 of 8 3 1435 words Type here to search wwwh 1) Suppose that Y₁, Y2, Yn is a random sample from a population with probability density function Find the Maximum Likelihood Estimator of B. 11 Normal No Spac.... Heading 1 Heading 2 Styles 1 1-8 f(y)=[By 0<y<1; B>0 0, English (South Africa) C Accessibility: Unavailable. O 2) Suppose that a random sample X₁X₂....X₁0 is from a poison distribution with mean 8. It is desired to test a null hypothesis Ho:0= 0.1 against alternative H₁: 0 = 0.5 at a level of significance 3) The probability density function for Y is given by 21 a) Use Neyman Raphson method to show that the best test or uniformly most powerful test rejects Ho if xc where c satisfies the probability equation a = P(₁²1x₁²c|0 = 0.1) b) If c = 3, show that Type I error is 0.0803 for the test in part a). Hint: 1X has a poisson distribution with mean 100. W elsewhere Use free at Office.com 26°C Title Subtitle Subtle Em..... ADE 4 ENG I 15:58 2022/10/08 2
Transcribed Image Text:ter Font Paragraph eatures are disabled because your Office product is inactive. To use for free, sign in and use the Web version. Activate 2 of 8 3 1435 words Type here to search wwwh 1) Suppose that Y₁, Y2, Yn is a random sample from a population with probability density function Find the Maximum Likelihood Estimator of B. 11 Normal No Spac.... Heading 1 Heading 2 Styles 1 1-8 f(y)=[By 0<y<1; B>0 0, English (South Africa) C Accessibility: Unavailable. O 2) Suppose that a random sample X₁X₂....X₁0 is from a poison distribution with mean 8. It is desired to test a null hypothesis Ho:0= 0.1 against alternative H₁: 0 = 0.5 at a level of significance 3) The probability density function for Y is given by 21 a) Use Neyman Raphson method to show that the best test or uniformly most powerful test rejects Ho if xc where c satisfies the probability equation a = P(₁²1x₁²c|0 = 0.1) b) If c = 3, show that Type I error is 0.0803 for the test in part a). Hint: 1X has a poisson distribution with mean 100. W elsewhere Use free at Office.com 26°C Title Subtitle Subtle Em..... ADE 4 ENG I 15:58 2022/10/08 2
Expert Solution
Step 1

Given that, Y1,Y2,....Yn is a random same from a population with pdf:-  

f(y) =  1βy(1-ββ),        0<y<1 ,  β>0

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