exercise:8b408c8df0: Difference between revisions
From Stochiki
(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> Suppose that we have a sequence of occurrences. We assume that the time <math>X</math> between occurrences is exponentially distributed with <math>\lambda = 1/10</math>, so on the average, there is one occurrence every 10 minutes (see guide:52...") |
No edit summary |
||
| Line 5: | Line 5: | ||
\newcommand{\secstoprocess}{\all} | \newcommand{\secstoprocess}{\all} | ||
\newcommand{\NA}{{\rm NA}} | \newcommand{\NA}{{\rm NA}} | ||
\newcommand{\mathds}{\mathbb}</math></div> Suppose that we have a sequence of occurrences. We assume | \newcommand{\mathds}{\mathbb}</math></div> Suppose that we have a sequence of occurrences. We assume that the time <math>X</math> between occurrences is exponentially distributed with <math>\lambda = 1/10</math>, so on the average, there is one occurrence every 10 minutes (see [[guide:523e6267ef#exam 2.2.7.5 |Example]]). | ||
that the time <math>X</math> between occurrences is exponentially distributed with <math>\lambda = 1/10</math>, | |||
so on the average, there is one occurrence every 10 minutes (see [[guide:523e6267ef#exam 2.2.7.5 |Example]]). | |||
You come upon this system at time 100, and wait until the next occurrence. Make a conjecture | You come upon this system at time 100, and wait until the next occurrence. Make a conjecture | ||
concerning how long, on the average, you will have to wait. Write a program to see if | concerning how long, on the average, you will have to wait. Write a program to see if | ||
your conjecture is right. | your conjecture is right. | ||
Latest revision as of 22:39, 12 June 2024
[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]
Suppose that we have a sequence of occurrences. We assume that the time [math]X[/math] between occurrences is exponentially distributed with [math]\lambda = 1/10[/math], so on the average, there is one occurrence every 10 minutes (see Example).
You come upon this system at time 100, and wait until the next occurrence. Make a conjecture concerning how long, on the average, you will have to wait. Write a program to see if your conjecture is right.