Problem 8 Suppose that X1, X2, X10 are iid exponential random variables. a. What is the joint density of X1, X 10 at x1, ... , . · , X10? b. Show that the likelihood ratio test for the null hypothesis...

Problem 8<br>Suppose that X1, X2,<br>X10 are iid exponential random variables.<br>a. What is the joint density of X1,<br>X 10 at x1, ... , .<br>· , X10?<br>b. Show that the likelihood ratio test for the null hypothesis 1 = 1.1 versus the alternate 1 = 2.1 with a = 0.05<br>can be written in the form: reject Ho when S < C for some constant C, where S = X1 + ·… + X10-<br>c. Find C that makes a = 0.05.<br>d. What is ß for your test?<br>

Extracted text: Problem 8 Suppose that X1, X2, X10 are iid exponential random variables. a. What is the joint density of X1, X 10 at x1, ... , . · , X10? b. Show that the likelihood ratio test for the null hypothesis 1 = 1.1 versus the alternate 1 = 2.1 with a = 0.05 can be written in the form: reject Ho when S < c="" for="" some="" constant="" c,="" where="" s="X1" +="" ·…="" +="" x10-="" c.="" find="" c="" that="" makes="" a="0.05." d.="" what="" is="" ß="" for="" your="">

Jun 05, 2022

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Problem 8 Suppose that X1, X2, X10 are iid exponential random variables. a. What is the joint density of X1, X 10 at x1, ... , . · , X10? b. Show that the likelihood ratio test for the null hypothesis...

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