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3) For known k ≥ 2 show that the negative binomial distribution with probability mass function, f(y, k, p) = = y = 0, 1, 2,.. 1 k k k (¹ + k − ¹) (¹ - 4 k)" (₁² k) ^ 1 Y u + + 1 belongs to the exponential family of distributions. Find the natural parameter for this distribution.

3) For known k ≥ 2 show that the negative binomial distribution with probability mass function, f(y, k, p) = = y = 0, 1, 2,.. 1 k k k (¹ + k − ¹) (¹ - 4 k)" (₁² k) ^ 1 Y u + + 1 belongs to the exponential family of distributions. Find the natural parameter for this distribution.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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3) For known k ≥ 2 show that the negative binomial distribution with probability mass function, f(y, k, μ) y = 0, 1, 2, .. = - 1 k k k (³ + k − ¹) (¹ − µ 4 k)" (1² k) " 1 Y + 1 belongs to the exponential family of distributions. Find the natural parameter for this distribution.
Transcribed Image Text:3) For known k ≥ 2 show that the negative binomial distribution with probability mass function, f(y, k, μ) y = 0, 1, 2, .. = - 1 k k k (³ + k − ¹) (¹ − µ 4 k)" (1² k) " 1 Y + 1 belongs to the exponential family of distributions. Find the natural parameter for this distribution.
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