Question: 7. suppose X1, . .. , An is a random sample from Poisson distribution with parameter 1, and Y1, ..., Yn is a random sample

7. suppose X1, . .. , An is a random sample from Poisson distribution with parameter 1, and Y1, ..., Yn is a random sample from Poisson distribution with parameter 12, and these samples are independent. We are interested in testing Ho : X1 = 12 versus Ha : 1 # 12. (a) Find an LRT statistic A for this problem. Simplify an expression for 2logA and give its approximate distribution. (b) suppose n = 20 and Xi+X2+. . .+X20 = 76 and Y1+Y2+. . .+Y20 = 98, use the likelihood ratio test to test the hypothesis Ho : 1 = 12 versus Ha : Al # 12 at the 5% significance level

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