AP Statistics Curriculum 2007 Exponential - Revision history

Tdlee: Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

2020-03-03T19:40:35Z

Text replacement - "{{translate|pageName=http://wiki.stat.ucla.edu/socr/" to ""{{translate|pageName=http://wiki.socr.umich.edu/"

2014-11-16T22:03:18Z

‎Exponential Distribution

2011-07-18T22:39:18Z

2011-07-18T22:39:05Z

2011-07-11T21:24:13Z

‎Exponential Distribution

2011-07-11T21:09:23Z

‎Applications

2011-07-11T20:55:12Z

‎Example

2011-07-11T20:51:52Z

‎Exponential Distribution

2011-07-11T20:51:09Z

‎Exponential Distribution

2011-07-11T20:50:24Z

‎Exponential Distribution

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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

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 ===Exponential Distribution===
-'''Definition''': Exponential distribution is a special case of the gamma distribution. Whereas the gamma distribution is the waiting time for more than one event, the exponential distribution describes the time between a single Poisson event.
+'''Definition''': Exponential distribution, also known as Mean-Time-To-Failure distribution, is a special case of the gamma distribution. Whereas the gamma distribution is the waiting time for more than one event, the exponential distribution describes the time between a single Poisson event.
 <br />'''Probability density function''': For <math>X\sim \operatorname{Exponential}(\lambda)\!</math>, the exponential probability density function is given by

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	* SOCR Home page: http://www.socr.ucla.edu		* SOCR Home page: http://www.socr.ucla.edu

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 ===Exponential Distribution===
 '''Definition''': Exponential distribution is a special case of the gamma distribution. Whereas the gamma distribution is the waiting time for more than one event, the exponential distribution describes the time between a single Poisson event.
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 The figure below shows this result using [http://socr.ucla.edu/htmls/dist/Exponential_Distribution.html SOCR distributions]
 <center>[[Image:Exponential.jpg|600px]]</center>

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 '''Definition''': Exponential distribution is a special case of the gamma distribution. Whereas the gamma distribution is the waiting time for more than one event, the exponential distribution describes the time between a single Poisson event.
-<br />'''Probability density function''': For <math>X\sim Exponential(\lambda)\!</math>, the exponential probability density function is given by
+<br />'''Probability density function''': For <math>X\sim \operatorname{Exponential}(\lambda)\!</math>, the exponential probability density function is given by
 :<math>\lambda e^{-\lambda x}\!</math>

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 *The height of various molecules in a gas at a fixed temperature and pressure in a uniform gravitational field
 *The monthly and annual maximum values of daily rainfall and river discharge volumes
 ===Example===

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 Suppose you usually get 2 phone calls per hour. Compute the probability that a phone call will arrive within the next hour.
-phone calls per hour means that we would expect one phone call every 1/2 hour so <math>\lambda=0.5</math>. We can then compute this as follows:
+phone calls per hour means that we would expect one phone call every 1/2 hour so <font size="3"><math>\lambda=0.5</math></font>. We can then compute this as follows:
 :<math>P(0\le X\le 1)=\sum_{x=0}^1 0.5e^{-0.5x}=0.393469</math>

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 where
 *e is the natural number (e = 2.71828…)
-*<math>\lambda</math> is the mean time between events
+*<font size="3"><math>\lambda</math></font> is the mean time between events
 *x is a random variable
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 where
 *e is the natural number (e = 2.71828…)
-*<math>\lambda</math> is the mean time between events
+*<font size="3"><math>\lambda</math></font> is the mean time between events
 *x is a random variable
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 :<math>Var(X)=\frac{1}{\lambda^2}</math>
 ===Applications===