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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Revision as of 20:03, 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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