Problem 1. Consider independent samples, X1, . , Xn from the density few,1 and Y1, . , Yn from the density f92,y2, where M9 far/(x) = $V+lllm 2...

Please help me to do this statistic problem about test hypothesis and the LRT test. Thanks!!!!!!!!!

Problem 1. Consider independent samples, X1, . . . , Xn from the density few,1 and Y1, . . . , Yn from the density f92,y2, whereM9"far/(x) = $V+lllm 2 6] for 0 > 0 and 1/ > 0. Consider testing H0 : (61,111) = (02,112) versus H1 : (61,121) 7£ (02,122). Useresults from Example 2 from the Handout on LRT in solving the following. (1) Show that the random variables are independent and obtain their marginal distributions.(2) Derive the LR test statistic A.(3) Find the LR test of size a = .02.