4 Let Y₁, Y., Y, constitute a random sample from the probability density function given by f(y)=(-y), 0≤ y ≤0, :{(²³) elsewhere. a Find an estimator for by using the method of moments.
4 Let Y₁, Y., Y, constitute a random sample from the probability density function given by f(y)=(-y), 0≤ y ≤0, :{(²³) elsewhere. a Find an estimator for by using the method of moments.
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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![**Problem 9.74**
Let \( Y_1, Y_2, \ldots, Y_n \) constitute a random sample from the probability density function given by
\[
f(y \mid \theta) =
\begin{cases}
\left( \frac{2}{\theta^2} \right) (\theta - y), & 0 \leq y \leq \theta, \\
0, & \text{elsewhere}.
\end{cases}
\]
**Tasks:**
a. Find an estimator for \( \theta \) by using the method of moments.
b. Is this estimator a sufficient statistic for \( \theta \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F763773a4-b59e-428b-8a3f-bc3dd5fb97d6%2F57bcd238-6737-4f9d-b749-e0faf535584f%2Fepn6zw5_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 9.74**
Let \( Y_1, Y_2, \ldots, Y_n \) constitute a random sample from the probability density function given by
\[
f(y \mid \theta) =
\begin{cases}
\left( \frac{2}{\theta^2} \right) (\theta - y), & 0 \leq y \leq \theta, \\
0, & \text{elsewhere}.
\end{cases}
\]
**Tasks:**
a. Find an estimator for \( \theta \) by using the method of moments.
b. Is this estimator a sufficient statistic for \( \theta \)?
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