Please see attached mathematical statistics question below. How to show the unbiased estimator of theta has variance2theta^2/n. Please do not reject question if you do not know how to solve this problem. Allow another expert a chance to answer this question. **Unbiased Estimator Problem**Let $ X_1, \ldots, X_n $ denote a random sample from a normal distribution with mean zero and variance $ \theta > 0 $. Show that $ \frac{1}{n} \sum_{i=1}^{n} X_i^2 $ is an unbiased estimator of $ \theta $ and has variance $ 2\theta^2 / n $.

It is a fact of statistics . It is widely used in probability .

Answered: Let X1,..., Xn denote a random sample…

Let X1,..., Xn denote a random sample from a normal distribution with mean zero and variance 0 > 0. Show that ", X? is an unbiased estimator of 0 and has variance 26 /n.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

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Please see attached mathematical statistics question below.

How to show the unbiased estimator of theta has variance
2theta^2/n.

Please do not reject question if you do not know how to solve this problem. Allow another expert a chance to answer this question.

**Unbiased Estimator Problem**

Let $ X_1, \ldots, X_n $ denote a random sample from a normal distribution with mean zero and variance $ \theta > 0 $. Show that $ \frac{1}{n} \sum_{i=1}^{n} X_i^2 $ is an unbiased estimator of $ \theta $ and has variance $ 2\theta^2 / n $.

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