Question: Let X1, X2, . . . , Xn denote a random sample from a population having a Poisson distribution with mean ?. Let X1, X2,

Let X1, X2, . . . , Xn denote a random sample from a population having a Poisson distribution with mean ?.

Let X1, X2, ..., Xn denote a random sample from a population having a Poisson distribution with mean 1. (a) Find the form of the rejection region for a most powerful test of Ho : A = do against H1 : 1 = 1, where I > do. (b) Recall that E X; has a Poisson distribution with mean nd. In- dicate how this information can be used to find any constants associated with the rejection region in part (a). (c) Is the test derived in part (a) uniformly most powerful for testing Ho : A = do against H1 : > > do? Why? (d) Find the form of the rejection region for a most powerful test of Ho : A = do against H1 : 1 = 1, where I

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