Find the Maximum Likelihood Estimator (MLE) of θ.
MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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- Define a random variable X as the proportion of voters in various districts that support Republican candidates for local offices. Research suggests that the
pdf of x is f(x) = θxθ-1 , where 0 < x < 1 and θ > 0. To estimate the parameter θ, a random sample of 10 districts was obtained, and their proportions of Republican support are: 0.42, 0.69, 0.40, 0.55, 0.66, 0.37, 0.63, 0.47, 0.44, 0.57. Find the Maximum Likelihood Estimator (MLE) of θ.
![1. Define a random variable X as the proportion of voters in various districts that support
Republican candidates for local offices. Research suggests that the pdf of x is f(x) = 0x°-1 , where
0<x<1 and e > 0. To estimate the parameter 0, a random sample of 10 districts was obtained,
%3D
and their proportions of Republican support are: 0.42, 0.69, 0.40, 0.55, 0.66, 0.37, 0.63, 0.47,
0.44, 0.57. Find the Maximum Likelihood Estimator (MLE) of 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce9942b2-0b4c-4d97-8b84-b9459bf26205%2F9f2c1153-7cdb-4ce2-b4c3-99a9b6dcaf38%2Fk9vgero_processed.png&w=3840&q=75)
Transcribed Image Text:1. Define a random variable X as the proportion of voters in various districts that support
Republican candidates for local offices. Research suggests that the pdf of x is f(x) = 0x°-1 , where
0<x<1 and e > 0. To estimate the parameter 0, a random sample of 10 districts was obtained,
%3D
and their proportions of Republican support are: 0.42, 0.69, 0.40, 0.55, 0.66, 0.37, 0.63, 0.47,
0.44, 0.57. Find the Maximum Likelihood Estimator (MLE) of 0.
![1. Define a random variable X as the proportion of voters in various districts that support
Republican candidates for local offices. Research suggests that the pdf of x is f(x) = 0x°-1 , where
0<x<1 and e > 0. To estimate the parameter 0, a random sample of 10 districts was obtained,
%3D
and their proportions of Republican support are: 0.42, 0.69, 0.40, 0.55, 0.66, 0.37, 0.63, 0.47,
0.44, 0.57. Find the Maximum Likelihood Estimator (MLE) of 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce9942b2-0b4c-4d97-8b84-b9459bf26205%2F9f2c1153-7cdb-4ce2-b4c3-99a9b6dcaf38%2F0b4g7r_processed.png&w=3840&q=75)
Transcribed Image Text:1. Define a random variable X as the proportion of voters in various districts that support
Republican candidates for local offices. Research suggests that the pdf of x is f(x) = 0x°-1 , where
0<x<1 and e > 0. To estimate the parameter 0, a random sample of 10 districts was obtained,
%3D
and their proportions of Republican support are: 0.42, 0.69, 0.40, 0.55, 0.66, 0.37, 0.63, 0.47,
0.44, 0.57. Find the Maximum Likelihood Estimator (MLE) of 0.
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