Consider a random sample X₁, X2,..., Xn from the following pdf (0x0-1 0≤x≤1 f(x) = {0x0. otherwise where 0 > 0. Find the maximum likelihood estimator for 0.
Consider a random sample X₁, X2,..., Xn from the following pdf (0x0-1 0≤x≤1 f(x) = {0x0. otherwise where 0 > 0. Find the maximum likelihood estimator for 0.
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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### Finding the Maximum Likelihood Estimator (MLE)
Consider a random sample \(x_1, x_2, ..., x_n\) from the following probability density function (pdf):
\[
f(x) =
\begin{cases}
\theta x^{\theta - 1} & \text{if } 0 \leq x \leq 1 \\
0 & \text{otherwise}
\end{cases}
\]
where \(\theta > 0\).
Find the maximum likelihood estimator for \(\theta\).
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Transcribed Image Text:---
### Finding the Maximum Likelihood Estimator (MLE)
Consider a random sample \(x_1, x_2, ..., x_n\) from the following probability density function (pdf):
\[
f(x) =
\begin{cases}
\theta x^{\theta - 1} & \text{if } 0 \leq x \leq 1 \\
0 & \text{otherwise}
\end{cases}
\]
where \(\theta > 0\).
Find the maximum likelihood estimator for \(\theta\).
---
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