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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
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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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.
Transcribed Image Text: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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