e. Let Xv"- Xn be i.i.d. . Y1,'..,Ym be i.i.d. likelihood random variables from normal distribution with mean 1'1 and variance of and random variables from normal distribution with mean p2 and variance 6:. Find the ratio test for testing Ho \"'1 : p2 , of : 0'; against all alternatives. The two samples are independent. (1. Let )(1,...,X10 be i'i.d. Bernoulli(p) random variables. Find the most powerful test of size a : 0.0547 for testing H,J : p = % against Ho :13 = %. Find the power of this test . e. Suppose that X],...,Xn are i.i.d. exponential random variables with EXZ, :13 ti where $1,...,t constants, andB > 0 is an unknown (See also exam 2, problem n are known 1 n X, parameter . It can be shown the MLE of is given byh 2c.) Suppose we want to test H0 13 = 1 against given by the likelihood ratio test. 1': (:1 z.- H 1. Find a test tatistic