# Difference between revisions of "SOCR EduMaterials Activities Exponential Distribution"

(→This is an activity to explore the Exponential Distribution: Learn how to compute probabilities, densities, and percentiles.) |
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* '''Description''': You can access the applet for the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html Exponential Distributions] | * '''Description''': You can access the applet for the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html Exponential Distributions] | ||

+ | * Here is the shape of the exponential distribution (this is a snpashot from the SOCR website: | ||

− | + | <center>[[Image:SOCR_Activities_DieCoinExperiment_Christou_092206_Fig1.jpg |600px]]</center> | |

− | + | ||

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− | + | * '''Exercise 1:''' Graph and print: | |

− | + | a. exp(0.2) | |

− | + | b. exp(1) | |

− | + | c. exp(10) | |

− | + | ||

− | + | * '''Exercise 2:''' Locate the maximum density for each one of these distributions. | |

+ | |||

+ | * '''Exercise 3:''' Find the height of the density at 3 values of X (one near 0, one near the mean, and one towards the tail of the distribution). | ||

+ | |||

+ | * '''Exercise 4:''' Find one percentile for each of these distributions and record them on the printouts. Verify these percentiles using the formula we discussed in class: | ||

\[ | \[ | ||

x_p=\frac{ln(1-\frac{p}{100})}{-\lambda} | x_p=\frac{ln(1-\frac{p}{100})}{-\lambda} | ||

\] | \] | ||

− | + | ||

+ | * '''Exercise 5:''' Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula: | ||

\[ | \[ | ||

P(X \le x)=1-e^{-\lambda x} | P(X \le x)=1-e^{-\lambda x} | ||

\] | \] | ||

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<hr> | <hr> |

## Revision as of 21:03, 23 September 2006

## This is an activity to explore the Exponential Distribution: Learn how to compute probabilities, densities, and percentiles.

**Description**: You can access the applet for the Exponential Distributions

- Here is the shape of the exponential distribution (this is a snpashot from the SOCR website:

Error creating thumbnail: File missing

**Exercise 1:**Graph and print:

a. exp(0.2) b. exp(1) c. exp(10)

**Exercise 2:**Locate the maximum density for each one of these distributions.

**Exercise 3:**Find the height of the density at 3 values of X (one near 0, one near the mean, and one towards the tail of the distribution).

**Exercise 4:**Find one percentile for each of these distributions and record them on the printouts. Verify these percentiles using the formula we discussed in class:

\[ x_p=\frac{ln(1-\frac{p}{100})}{-\lambda} \]

**Exercise 5:**Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula:

\[ P(X \le x)=1-e^{-\lambda x} \]

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

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