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Let X1,..., Xn be independent binomial rvs with n = 10 and p = 0.8. a. What are the mean u and the sd o of the Binom(10,0.8) distribution? b. How large does n need to be before the pdf of X-u is approximately that of a standard normal rv?

Let X1,..., Xn be independent binomial rvs with n = 10 and p = 0.8. a. What are the mean u and the sd o of the Binom(10,0.8) distribution? b. How large does n need to be before the pdf of X-u is approximately that of a standard normal rv?

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
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Let \( X_1, \ldots, X_n \) be independent binomial random variables (rvs) with \( n = 10 \) and \( p = 0.8 \). a. What are the mean \( \mu \) and the standard deviation \( \sigma \) of the \( \text{Binom}(10, 0.8) \) distribution? b. How large does \( n \) need to be before the probability density function (pdf) of \( \frac{\overline{X} - \mu}{\sigma / \sqrt{n}} \) is approximately that of a standard normal rv?
Transcribed Image Text:Let \( X_1, \ldots, X_n \) be independent binomial random variables (rvs) with \( n = 10 \) and \( p = 0.8 \). a. What are the mean \( \mu \) and the standard deviation \( \sigma \) of the \( \text{Binom}(10, 0.8) \) distribution? b. How large does \( n \) need to be before the probability density function (pdf) of \( \frac{\overline{X} - \mu}{\sigma / \sqrt{n}} \) is approximately that of a standard normal rv?
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