2. Let X₁,. X₁ be a random sample from N(u, o²) distribution.-1(a) Show that (X, S²) is a sufficient statistic for (u, o²), where X = n−¹ Σï=1 Xiand S² = (n − 1)-¹ Σ²²_₁(Xi — X)².(b)Find the best unbiased estimator for oº, where p > 0 and it is not necessarilyan integer.

The random sample is .The random sample was selected from .Here, is the population mean and is the…

2. Let X₁,..., Xn be a random sample from N(u, o²) distribution. ,-1 (a) Show that (X, S²) is a sufficient statistic for (u, o²), where X = n¯¹ Σ=₁ Xi and S² = (n − 1)-¹ Σï1(Xi − X)². - (b) Find the best unbiased estimator for op, where p > 0 and it is not necessarily an integer.

2. Let X₁,..., Xn be a random sample from N(u, o²) distribution. ,-1 (a) Show that (X, S²) is a sufficient statistic for (u, o²), where X = n¯¹ Σ=₁ Xi and S² = (n − 1)-¹ Σï1(Xi − X)². - (b) Find the best unbiased estimator for op, where p > 0 and it is not necessarily an integer.

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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Question

2. Let X₁,. X₁ be a random sample from N(u, o²) distribution.
-1
(a) Show that (X, S²) is a sufficient statistic for (u, o²), where X = n−¹ Σï=1 Xi
and S² = (n − 1)-¹ Σ²²_₁(Xi — X)².
(b)
Find the best unbiased estimator for oº, where p > 0 and it is not necessarily
an integer.

Expert Solution

Step 1: Write the given information.

The random sample is $X subscript 1 comma space X subscript 2 comma space... comma space X subscript n$ .

The random sample was selected from $N open parentheses mu comma space sigma squared close parentheses$ .

Here, $mu$ is the population mean and $sigma squared$ is the population variance.

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