Let \( Y_1, Y_2, \ldots, Y_n \) denote a random sample from the probability density function\[f(y \mid \theta) = \begin{cases} e^{-(y - \theta)}, & y \geq \theta, \\0, & \text{elsewhere}.\end{cases}\]Show that \( Y_{(1)} = \min(Y_1, Y_2, \ldots, Y_n) \) is sufficient for \( \theta \). **Task:**Find a function of \( Y_{(1)} \) that is an MVUE for \( \theta \).---**Explanation:**- **\( Y_{(1)} \):** This indicates the smallest order statistic from a sample.- **MVUE:** Stands for Minimum Variance Unbiased Estimator, which is an estimator that has the lowest variance among all unbiased estimators for a parameter \( \theta \).In statistical estimation, identifying an MVUE is crucial because it ensures that we estimate parameters as accurately and precisely as possible without systematic error.

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Answered: Let Y;. Yz. --.. Y, denote a random…

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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(2) JAL ?Q13) Consider the following probability density function, what is the F(14) 0.22 X= 7 0.22 0.05 0.05 0.06 X = 9 X= 11 f (x) X = 13 15 0.33 X = 17 0.06 0.01 X = 19 X = 23 0.54 0.6 0.93 0.99 EN LG
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Let W₁ < W₂ < ... < Wn be the order statistics of n independent observations from a U(0, 1) distribution. (a) Find the pdf of W₁ and that of Wn. (b) Use the results of (a) to verify that E (W₁) = 1/(n+1) and E(Wn) = n/(n+1).
5

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Let Y;. Yz. --.. Y, denote a random sample from the probability density function e , y20, 0, elsewhere. Show that Y1) = min(Y1, Y2, .... Y,) is sufficient for e. %3!