MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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11. Suppose \( X_1, X_2, \ldots, X_n \) are i.i.d. from a distribution with pdf:

\[
f(x) = \theta e^{\theta} x^{-\theta - 1} \quad \text{for } x > e
\]

\[
f(x) = 0 \quad \text{otherwise}
\]

i. What is the maximum likelihood estimator of \( \theta \)? [You do not have to check the second derivative to verify that it is a maximum.]

ii. What is the maximum likelihood estimator of \( e^\theta \)?
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Transcribed Image Text:11. Suppose \( X_1, X_2, \ldots, X_n \) are i.i.d. from a distribution with pdf: \[ f(x) = \theta e^{\theta} x^{-\theta - 1} \quad \text{for } x > e \] \[ f(x) = 0 \quad \text{otherwise} \] i. What is the maximum likelihood estimator of \( \theta \)? [You do not have to check the second derivative to verify that it is a maximum.] ii. What is the maximum likelihood estimator of \( e^\theta \)?
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