Suppose that X ~ Gamma(3, b), with pdf-brf(r\b) =2on a > 0,where b> 0. It is required to test the null hypothesis Họ : b= bo against thealternative hypothesis H1 : b = b1, based on a random sample #1,x2,..., Tn.(a) Find the log-likelihood l(b).(b) Let LR be the likelihood ratio L(b1)/L(bo). Show that the log of thelikelihood ratio islog(LR) = 3n logbo(2)- (b1 – bo) ri-i=1(c) Using the expression for log(LR) that you obtained in part (b), showthat the rejection region R= {x : log(LR) > d} for the test is of theform T< d if b1 > bo. Hence give c' in terms of d.

From the given information, X~Gamma3, b with pdf fx|b=b32x2e-bx, x>0 Null Hypothesis: H0:b=b0…

Answered: Suppose that X ~ Gamma(3, b), with pdf…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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