exercise:C269f2d701: Difference between revisions
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(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...") |
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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 | |||
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> | 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 | 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 | of the densities in [[exercise:088f67773d |Exercise]]. Compute their sum <math>S_n</math>, | ||
repeat this experiment 1000 times, and make up a bar graph of 20 bars of the | 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? | results. How large must <math>n</math> be before you get a good fit? | ||
Latest revision as of 00:26, 15 June 2024
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. 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?