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 supportRepublican candidates for local offices. Research suggests that the pdf of x is f(x) = 0x°-1 , where0 0. To estimate the parameter 0, a random sample of 10 districts was obtained,%3Dand 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 supportRepublican candidates for local offices. Research suggests that the pdf of x is f(x) = 0x°-1 , where0 0. To estimate the parameter 0, a random sample of 10 districts was obtained,%3Dand 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.

To determine the MLE we have to find the likelihood and log-likelihood functions.

Answered: Find the Maximum Likelihood Estimator…

Math

Statistics

Find the Maximum Likelihood Estimator (MLE) of θ.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 4CYU

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Question

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) = θx^θ-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.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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