Statistics : Neyman Factorization Theorem

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  Therefore by the Neyman Factorization criterion is a sufficient statistic for . By the additive property of Gamma random variable we have has .

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  Therefore by the Neyman Factorization criterion is a sufficient statistic for . By the additive property of Binomial random variable we have has a Binomial distribution with parameter and .

• Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.

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• the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.

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  50267 Euclidean algorithm, primes and unique factorization, congruence Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial

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• Neyman Pearson Lemma

  2063 Proving Neyman-Pearson Lemma Prove the Neyman-Pearson Lemma. Please see attached files The solution proves the Neyman-Pearson Lemma.

• Sufficiency

  Use Neyman's Factorization Theorem. See attachment please. Hope it helps. The solution is provided in an attachment, answered step-by-step equationally.