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7.2.1. Let X₁, X2,..., Xn be iid N(0, 0), 0 <0 < . Show that 1X² is a sufficient statistic for 0. 7.2.2. Prove that the sum of the observations of a random sample of size n from a Poisson distribution having parameter 0, 0< 0

7.2.1. Let X₁, X2,..., Xn be iid N(0, 0), 0 <0 < . Show that 1X² is a sufficient statistic for 0. 7.2.2. Prove that the sum of the observations of a random sample of size n from a Poisson distribution having parameter 0, 0< 0

MATLAB: An Introduction with Applications
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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**7.2.1.** Let \( X_1, X_2, \ldots, X_n \) be iid \( N(0, \theta) \), \( 0 < \theta < \infty \). Show that \( \sum_{i=1}^n X_i^2 \) is a sufficient statistic for \( \theta \). **7.2.2.** Prove that the sum of the observations of a random sample of size \( n \) from a Poisson distribution having parameter \( \theta \), \( 0 < \theta < \infty \), is a sufficient statistic for \( \theta \). --- The content above includes two statistical problems: 1. The first problem asks to show that the sum of squares of \( n \) independent and identically distributed (iid) samples from a normal distribution \( N(0, \theta) \) is a sufficient statistic for \( \theta \). 2. The second problem involves proving that the sum of a random sample from a Poisson distribution with parameter \( \theta \) is a sufficient statistic for \( \theta \). There are no graphs or diagrams in this image.
Transcribed Image Text:**7.2.1.** Let \( X_1, X_2, \ldots, X_n \) be iid \( N(0, \theta) \), \( 0 < \theta < \infty \). Show that \( \sum_{i=1}^n X_i^2 \) is a sufficient statistic for \( \theta \). **7.2.2.** Prove that the sum of the observations of a random sample of size \( n \) from a Poisson distribution having parameter \( \theta \), \( 0 < \theta < \infty \), is a sufficient statistic for \( \theta \). --- The content above includes two statistical problems: 1. The first problem asks to show that the sum of squares of \( n \) independent and identically distributed (iid) samples from a normal distribution \( N(0, \theta) \) is a sufficient statistic for \( \theta \). 2. The second problem involves proving that the sum of a random sample from a Poisson distribution with parameter \( \theta \) is a sufficient statistic for \( \theta \). There are no graphs or diagrams in this image.
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