Problem 1 Let X1,X2, . , Xn i'g' exponentialw) and Y1, Y2, . , Yn i'i-Ei' errpmzentialm]. Find the likelihood ratio test (ILRT) of Hg : 6' 2 pi vs. 6...

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].