Let Y, represent the ith normal population with unknown mean #4, and unknown varianceof for i=1,2. Consider independent random samples, Ya, Ya.Yin, of size n,, fromthe ith population with sample mean Y, and sample variance S?=(-)².(d) Define Vi, a function of S7, that has a chi-square distribution.(e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument.(f) Finda (1-a) x 100% confidence interval for of.

The random variable follows a normal distribution with a mean, and a standard deviation,…

Answered: Let Y, represent the ith normal…

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

Let Y, represent the ith normal population with unknown mean #4, and unknown variance
of for i=1,2. Consider independent random samples, Ya, Ya.Yin, of size n,, from
the ith population with sample mean Y, and sample variance S?=(-)².
(d) Define Vi, a function of S7, that has a chi-square distribution.
(e) Is V₁ a pivotal function to find a confidence interval for o?? Explain with argument.
(f) Finda (1-a) x 100% confidence interval for of.

Expert Solution

Step 1: Write the given information.

The random variable $Y subscript i$ follows a normal distribution with a mean, $mu subscript i$ and a standard deviation, $sigma subscript i$ .

Symbolically, $Y subscript i tilde N open parentheses mu subscript i comma space sigma subscript i close parentheses$ where $i equals 1 comma space 2$ .

The sample size is $n subscript i$ .

The sample mean is $Y with bar on top subscript i$ .

The sample variance is $S subscript i superscript 2 equals fraction numerator 1 over denominator n subscript i minus 1 end fraction sum from j equals 1 to n subscript 1 of open parentheses Y subscript i j end subscript minus Y with bar on top close parentheses squared$ .