*9.52 Let Y₁, ₂,..., Y, be a random sample from a population with density function 3y² f(y|0) = 8³ 0≤y≤0, elsewhere. Show that Y() = max(Y₁, Y₂,..., Y,) is sufficient for 0.
*9.52 Let Y₁, ₂,..., Y, be a random sample from a population with density function 3y² f(y|0) = 8³ 0≤y≤0, elsewhere. Show that Y() = max(Y₁, Y₂,..., Y,) is sufficient 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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![**Exercise 9.52**
Let \( Y_1, Y_2, \ldots, Y_n \) be a random sample from a population with density function
\[
f(y \mid \theta) =
\begin{cases}
\frac{3y^2}{\theta^3}, & \text{for } 0 \leq y \leq \theta, \\
0, & \text{elsewhere}.
\end{cases}
\]
Show that \( Y_{(n)} = \max(Y_1, Y_2, \ldots, Y_n) \) is sufficient for \( \theta \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F763773a4-b59e-428b-8a3f-bc3dd5fb97d6%2Fac89364d-d646-4a74-9b87-30cfa538aa45%2F6saokaj_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise 9.52**
Let \( Y_1, Y_2, \ldots, Y_n \) be a random sample from a population with density function
\[
f(y \mid \theta) =
\begin{cases}
\frac{3y^2}{\theta^3}, & \text{for } 0 \leq y \leq \theta, \\
0, & \text{elsewhere}.
\end{cases}
\]
Show that \( Y_{(n)} = \max(Y_1, Y_2, \ldots, Y_n) \) is sufficient for \( \theta \).
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