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: | + | * Here is the shape of the exponential distribution (this is a snpashot from the SOCR website): |
<center>[[Image:SOCR_Activities_ExponentialDistribution_Christou_092206_Fig1.jpg |600px]]</center> | <center>[[Image:SOCR_Activities_ExponentialDistribution_Christou_092206_Fig1.jpg |600px]]</center> | ||
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* '''Exercise 1:''' Graph and print: | * '''Exercise 1:''' Graph and print: | ||
| − | a. exp(0.2) | + | **a. exp(0.2) |
| − | b. exp(1) | + | **b. exp(1) |
| − | c. exp(10) | + | **c. exp(10) |
* '''Exercise 2:''' Locate the maximum density for each one of these distributions. | * '''Exercise 2:''' Locate the maximum density for each one of these distributions. | ||
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* '''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: | * '''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: | ||
| − | + | ||
| + | |||
| + | <math> | ||
x_p=\frac{ln(1-\frac{p}{100})}{-\lambda} | x_p=\frac{ln(1-\frac{p}{100})}{-\lambda} | ||
| − | + | </math> | |
* '''Exercise 5:''' Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula: | * '''Exercise 5:''' Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula: | ||
| − | + | <math> | |
P(X \le x)=1-e^{-\lambda x} | P(X \le x)=1-e^{-\lambda x} | ||
| − | + | </math> | |
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* SOCR Home page: http://www.socr.ucla.edu | * SOCR Home page: http://www.socr.ucla.edu | ||
| − | {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title= | + | {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_Exponential_Distribution}} |
Latest revision as of 14:01, 8 July 2007
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):
- 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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