Please explain in details, and I don't want answers copied from other WEBSITES ANSWERS. Thanks!

Let X1, ..., Xx be a random sample from the Poisson distribution e-ofx f(x; 0) = (o. 1. 2. ...) (x). x! (a) Find the UMP test of # o: 0 = 0. versus # 1: 0 > 0%, and sketch the power function for do=1 and n=25. (Use the central-limit theorem. Pick a = .05.) (b) Test Ho: 0 = 0. versus #1: 0 # 0. Find the general form of the critical region corresponding to the test arrived at using the generalized likelihood- ratio principle. (The critical region should be defined in terms of [ X, .) (c) A reasonable test of # o: 0 = 0. versus # 1: 0 # 0. would be the following: Reject if | X - Go| 2 K. For a = .05, find K so that P[reject Hol H o]= .05. (Assume that n is large enough so that the central-limit theorem can be used to find an approximation to K.)