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nspection trials are carried out in a factory to assess the quality of products. In each trial r; products are tested and Y;, the Bin(ri, p), where p is the umber of satisfactory items in the trial, is assumed to follow the binomial model Y₁ roportion of satisfactory items in the production process. Using inspection data (r₁, y₁), (r2, y2), ..., (rn, Yn) and assuming independent trials, the following log-likelihood for p was obtained 1(p; data)= 19.5678 +40 log(p) + 10 · log(1 − p). ).

nspection trials are carried out in a factory to assess the quality of products. In each trial r; products are tested and Y;, the Bin(ri, p), where p is the umber of satisfactory items in the trial, is assumed to follow the binomial model Y₁ roportion of satisfactory items in the production process. Using inspection data (r₁, y₁), (r2, y2), ..., (rn, Yn) and assuming independent trials, the following log-likelihood for p was obtained 1(p; data)= 19.5678 +40 log(p) + 10 · log(1 − p). ).

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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find the maximum likelihood estimate ?̂

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 Y₁ Bin(ri, p), where p is the proportion of satisfactory items in the production process. Using inspection data (r1, y₁), (r2, Y2), …., (˜n, Yn) and assuming independent trials, the following log-likelihood for p was obtained l(p; data) = 19.5678 +40 · log(p) + 10 · log(1 − 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 Y₁ Bin(ri, p), where p is the proportion of satisfactory items in the production process. Using inspection data (r1, y₁), (r2, Y2), …., (˜n, Yn) and assuming independent trials, the following log-likelihood for p was obtained l(p; data) = 19.5678 +40 · log(p) + 10 · log(1 − p).
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