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We consider here the Negative Binomial Distribution Ninom(m, p), with fixed, known m E N. Recall that the PMF of that Distribution is given by ƒ(x\m,p) = (x − = (x − m-1 Also recall that for X~ NBinom(m, p), Show Transcribed Text ¹) · ¹) .pm . (1 - p)²-m, E(X) m == P xm, m+ 1, m+2,.... and Var (X): = a. Find the MLE Estimator for p b. Estimate the Variance of that Distribution using the MLE method; c. Calculate the Fisher Information for p. Show and explain below all your steps. m(1 − p). p²

We consider here the Negative Binomial Distribution Ninom(m, p), with fixed, known m E N. Recall that the PMF of that Distribution is given by ƒ(x\m,p) = (x − = (x − m-1 Also recall that for X~ NBinom(m, p), Show Transcribed Text ¹) · ¹) .pm . (1 - p)²-m, E(X) m == P xm, m+ 1, m+2,.... and Var (X): = a. Find the MLE Estimator for p b. Estimate the Variance of that Distribution using the MLE method; c. Calculate the Fisher Information for p. Show and explain below all your steps. m(1 − p). p²

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 26E
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We consider here the Negative Binomial Distribution NBinom(m, p), with fixed, known m E N. Recall that the PMF of that Distribution is given by ƒ(x\m, p) = (x − ¹) · • p. (1-p) x-m, Also recall that for X NBinom (m, p), E(X) Show Transcribed Text 3 m P c and a. Find the MLE Estimator for p; b. Estimate the Variance of that Distribution using the MLE method; c. Calculate the Fisher Information for p. Show and explain below all your steps. x = m, m+ 1, m + 2,.... Var (X) = = m(1 − p) p²
Transcribed Image Text:We consider here the Negative Binomial Distribution NBinom(m, p), with fixed, known m E N. Recall that the PMF of that Distribution is given by ƒ(x\m, p) = (x − ¹) · • p. (1-p) x-m, Also recall that for X NBinom (m, p), E(X) Show Transcribed Text 3 m P c and a. Find the MLE Estimator for p; b. Estimate the Variance of that Distribution using the MLE method; c. Calculate the Fisher Information for p. Show and explain below all your steps. x = m, m+ 1, m + 2,.... Var (X) = = m(1 − p) p²
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