Problem (25 points) This problem involves hypothesis testing of exponentially distributed data. Let Y1, Y2, . .. , Yn be i.i.d. random variables from an exponential distribution with rate parameter ). The density of an exponential is given as: f(Yi) = )exp(-)Yi), i = 1, 2, . .. , n. We want to test the hypothesis that the data comes from a unit exponential, i.e. ) = 1. A. Find the MLE for 1 for the data Y1, Y2, . . . , Yn B. Calculate the likelihood under the null and under the MLE, and obtain the generalized likelihood ratio (GLR). C. How does the GLR depend on the data vector Y = {Y1, . .. , Yn}? This statistic is called a sufficient statistic for the rate parameter 1. Let us call it T( Y)