When the sample standard deviation \( S \) is based on a random sample from a normal population distribution, it can be shown that\[E(S) = \sqrt{\frac{2}{(n-1)}} \frac{\Gamma(n/2)}{\Gamma((n-1)/2)} \sigma\]Use this to obtain an unbiased estimator for \( \sigma \) of the form \( cS \). What is \( c \) when \( n = 18 \)? (Round your answer to four decimal places.)\[ \text{Input Box} \]\[ \text{Incorrect answer indicator (Red X)} \]**Need Help?**- **Read It** (button)- **Watch It** (button)### Explanation:This formula calculates the expected value of the sample standard deviation \( S \) for a normal population distribution. The equation uses the Gamma function \( \Gamma \) and involves the sample size \( n \).The task is to find a constant \( c \) such that \( cS \) is an unbiased estimator for the population standard deviation \( \sigma \), specifically when \( n = 18 \). The user is prompted to input an answer, which should be rounded to four decimal places. The presence of a red "X" indicates the inputted answer is incorrect. Additionally, resources are available through "Read It" and "Watch It" buttons for further help.

Answered: When the sample standard deviation S is…

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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