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6.5.6. Suppose a sufficient statistic exists for the parameter θ. Use Theorem 5.6.1 to show that the critical region of a likelihood ratio test will depend on the sufficient statistic.

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Answer:

Firstly, the defined parameters are X, Q, P,g, h, b

Let X1 = Q1,……..Xn, = Qn be a random sample of size n from the discrete  Px

Step-by-step explanation:

Let X1 = Q1,……..Xn, = Qn be a random sample of size n from the discrete  Px (k;θ) The statistic θ= h(X1,..., Xn) is sufficient for if and only if there are functions g[h(Q1...., Qn.);θ]and b(Q1.... Qn)   such that L(θ) = g(h(Q1. ..., Qn); ) b(Qi...., Qn)  where the function b(Qi.....Qn) does not associate  the parameter . A case holds in the continuous case.

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