IGNOU MTE 11 2018 - Obtain the maximum likelihood estimate of inbased on an independe

Question

Obtain the maximum likelihood estimate of $\theta$ in
$f(x,\theta ) = (1 + \theta ) x^\theta ,0 < x< 1$
based on an independent sample of size n.

14 Feb 2018

Answer :

Word Count : 311

The problem asks us to find the maximum likelihood estimate (MLE) of $\theta$ based on the probability density function (pdf): \[ f(x, \theta) = (1 + \theta) x^\theta, \quad 0 < x < 1 \] for an independent sample of size $n$. ### Steps to solve the problem: 1. Write the likelihood function: The likelihood function $L(\theta)$ for an independent sample $x_1, x_2, ..., x_n$ is the product

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