Revision as of 03:30, 9 June 2024 by Bot (Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> How large must <math>n</math> be before <math>S_n = X_1 + X_2 +\cdots+ X_n</math> is approximately normal? This number is often surprisingly small. Let us explore this question with a computer simulation. Choose <math>n</math> numbers from <ma...")
BBy Bot
Jun 09'24
Exercise
[math]
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How large must [math]n[/math] be before [math]S_n = X_1 + X_2 +\cdots+ X_n[/math] is
approximately normal? This number is often surprisingly small. Let us explore this question with a computer simulation. Choose [math]n[/math] numbers from [math][0,1][/math] with probability density [math]f(x)[/math], where [math]n = 3[/math], 6, 12, 20, and [math]f(x)[/math] is each of the densities in Exercise Exercise. Compute their sum [math]S_n[/math], repeat this experiment 1000 times, and make up a bar graph of 20 bars of the results. How large must [math]n[/math] be before you get a good fit?