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1. Fix r € N, and suppose that Y₁,..., Yn are independent and identically distributed NegBin(r, ) random variables, each with probability mass function given by ³x (1 10) = (u +r- (1 - 0) ³0⁰ for y N and unknown 0 € (0, 1). Here the number of successes r in the negative binomial is known.

1. Fix r € N, and suppose that Y₁,..., Yn are independent and identically distributed NegBin(r, ) random variables, each with probability mass function given by ³x (1 10) = (u +r- (1 - 0) ³0⁰ for y N and unknown 0 € (0, 1). Here the number of successes r in the negative binomial is known.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 19E
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1. Fix r € N, and suppose that Y₁,..., Yn are independent and identically distributed NegBin(r, ) random variables, each with probability mass function given by ¡v (u | 0) – (1 + r − ¹) (1 - fy y (1 - 0) ³0⁰ for y ¤ N and unknown 0 € (0, 1). Here the number of successes r in the negative binomial is known.
Transcribed Image Text:1. Fix r € N, and suppose that Y₁,..., Yn are independent and identically distributed NegBin(r, ) random variables, each with probability mass function given by ¡v (u | 0) – (1 + r − ¹) (1 - fy y (1 - 0) ³0⁰ for y ¤ N and unknown 0 € (0, 1). Here the number of successes r in the negative binomial is known.
(c) Using that E{T(Y)} for the parameter = = = (d) Using that Var(T(Y)) = in part (c). dA (or otherwise), write down an unbiased estimator (or otherwise), find the variance of your estimator 1+0 (e) Using that 0 = Write down the loglikelihood (o; y) for 6 and calculate = -E²(y) for 0. the Fisher information I() =
Transcribed Image Text:(c) Using that E{T(Y)} for the parameter = = = (d) Using that Var(T(Y)) = in part (c). dA (or otherwise), write down an unbiased estimator (or otherwise), find the variance of your estimator 1+0 (e) Using that 0 = Write down the loglikelihood (o; y) for 6 and calculate = -E²(y) for 0. the Fisher information I() =
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