exercise:9db99f5fb1: 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> Recall that if <math>X</math> is a random variable, the ''cumulative distribution function'' of <math>X</math> is the function <math>F(x)</math> defined by <math display="block"> F(x) = P(X \leq x)\ . </math> <ul><li> Let <math>S_n</math> be th...") |
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Recall that if <math>X</math> is a random variable, the ''cumulative distribution function'' of <math>X</math> is the function <math>F(x)</math> defined by | |||
function'' of <math>X</math> is the function <math>F(x)</math> defined by | |||
<math display="block"> | <math display="block"> | ||
F(x) = P(X \leq x)\ . | F(x) = P(X \leq x)\ . | ||
</math> | </math> | ||
<ul><li> Let <math>S_n</math> be the number of successes in <math>n</math> Bernoulli trials with | <ul style="list-style-type:lower-alpha"><li> Let <math>S_n</math> be the number of successes in <math>n</math> Bernoulli trials with | ||
probability <math>p</math> for success. Write a program to plot the cumulative distribution | probability <math>p</math> for success. Write a program to plot the cumulative distribution | ||
for <math>S_n</math>. | for <math>S_n</math>. | ||
Latest revision as of 22:59, 14 June 2024
Recall that if [math]X[/math] is a random variable, the cumulative distribution function of [math]X[/math] is the function [math]F(x)[/math] defined by
[[math]]
F(x) = P(X \leq x)\ .
[[/math]]
- Let [math]S_n[/math] be the number of successes in [math]n[/math] Bernoulli trials with probability [math]p[/math] for success. Write a program to plot the cumulative distribution for [math]S_n[/math].
- Modify your program in (a) to plot the
cumulative distribution [math]F_n^*(x)[/math] of the standardized random variable
[[math]] S_n^* = \frac {S_n - np}{\sqrt{npq}}\ . [[/math]]
- Define the normal distribution [math]N(x)[/math] to be the area under the normal curve up to the value [math]x[/math]. Modify your program in (b) to plot the normal distribution as well, and compare it with the cumulative distribution of [math]S_n^*[/math]. Do this for [math]n = 10, 50[/math], and [math]100[/math].