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Inspection trials are carried out in a factory to assess the quality of products. In each trial r, products are tested and Y₁, the number of satisfactory items in the trial, is assumed to follow the binomial model Y₁ ~ Bin(ri, p), where p is the proportion of satisfactory items in the production process. Using inspection data (rı, y₁), (r2, y2), ..., (rn, Yn) and assuming independent trials, the following log-likelihood for p was obtained 1(p; data) = 25.8392 + 35 · log(p) + 17. log(1 − p). A) Determine which of the following (r₁, y₁), (r2, y2), ..., (rn, yn) is the correct data that yields the given log-likelihood /(p; data). Note that you do not need to develop the likelihood from scratch, but to carefully look and use results shown in lectures, notes and exercises. B) Write the maximum likelihood estimate p.

Inspection trials are carried out in a factory to assess the quality of products. In each trial r, products are tested and Y₁, the number of satisfactory items in the trial, is assumed to follow the binomial model Y₁ ~ Bin(ri, p), where p is the proportion of satisfactory items in the production process. Using inspection data (rı, y₁), (r2, y2), ..., (rn, Yn) and assuming independent trials, the following log-likelihood for p was obtained 1(p; data) = 25.8392 + 35 · log(p) + 17. log(1 − p). A) Determine which of the following (r₁, y₁), (r2, y2), ..., (rn, yn) is the correct data that yields the given log-likelihood /(p; data). Note that you do not need to develop the likelihood from scratch, but to carefully look and use results shown in lectures, notes and exercises. B) Write the maximum likelihood estimate p.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
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Inspection trials are carried out in a factory to assess the quality of products. In each trial r¡ products are tested and Y;, the number of satisfactory items in the trial, is assumed to follow the binomial model Y; Bin(ri, p), where p is the proportion of satisfactory items in the production process. Using inspection data (rı, yı), (r2, Y2), …‚ (˜n, Yn) and assuming independent trials, the following log-likelihood for p was obtained ... l(p; data) = 25.8392 + 35 · log(p) + 17 · log(1 − p). A) Determine which of the following (r1, y₁), (r2, y2), …‚ (˜n, yn) is the correct data that yields the given log-likelihood 1(p; data). Note that you do not need to develop the likelihood from scratch, but to carefully look and use results shown in lectures, notes and exercises. B) Write the maximum likelihood estimate p.
Transcribed Image Text:Inspection trials are carried out in a factory to assess the quality of products. In each trial r¡ products are tested and Y;, the number of satisfactory items in the trial, is assumed to follow the binomial model Y; Bin(ri, p), where p is the proportion of satisfactory items in the production process. Using inspection data (rı, yı), (r2, Y2), …‚ (˜n, Yn) and assuming independent trials, the following log-likelihood for p was obtained ... l(p; data) = 25.8392 + 35 · log(p) + 17 · log(1 − p). A) Determine which of the following (r1, y₁), (r2, y2), …‚ (˜n, yn) is the correct data that yields the given log-likelihood 1(p; data). Note that you do not need to develop the likelihood from scratch, but to carefully look and use results shown in lectures, notes and exercises. B) Write the maximum likelihood estimate p.
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