**Title: Constructing an 80% Confidence Interval Using Pivotal Quantities****Content:**To determine an 80% confidence interval for the parameter \( \theta \), we utilize the pivotal quantity \( \frac{2Y}{\theta} \). This approach involves expressing the interval in terms of the observed value \( Y \).**Explanation:**- **Pivotal Quantity:** The expression \( \frac{2Y}{\theta} \) is used as a pivotal quantity, which is a function of the observed data and the parameter of interest. A pivotal quantity typically follows a known probability distribution that does not depend on the unknown parameter.- **Confidence Interval:** A confidence interval provides a range of values for the unknown parameter \( \theta \) with a specified probability, here 80%. This means that there is an 80% chance that the interval contains the true value of \( \theta \).**Steps:**1. Calculate the observed value of the statistic \( Y \).2. Use the pivotal quantity \( \frac{2Y}{\theta} \) to help express the confidence interval.3. Solve the inequalities associated with the confidence level to obtain the bounds of the interval for \( \theta \).This methodology provides a structured way to estimate the parameter using observed data, ensuring accuracy within the specified level of confidence. Let \( Y \) be an exponential random variable with (unknown) mean \( \theta \).

Answered: Let Y be an exponential random variable…

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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Let Y be an exponential random variable with (unknown) mean 0.