Problem 1 Let X1 X2 Xn I G Exponentialw And Y1 Y2 Yn I I Ei Errpmzentialm Find T

This question that has been attached is from Biostatistical theory course.
Problem 1 Let X1,X2, . . . , Xn i’g’ exponentialw) and Y1, Y2, . . . , Yn i’i-Ei’ errpmzentialm]. i. Find the likelihood ratio test (ILRT) of Hg : 6′ 2 pi vs. H1 : 6 7E ,u. ii. Based on the LRT in (a), find the rejection region for a test With the the test statistic T = %. iii. Find the null distribution of T (hint: first prove the sum of i.i.d. exponential random variables has agamma distribution].
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