Difference between revisions of "SOCR EduMaterials Activities ExpDist"
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| − | == This is an activity to explore the Exponential Distribution: Learn how to compute probabilities, densities, and percentiles | + | == 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 [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html Exponential Distributions] | ||
| + | * Graph and print | ||
| + | **<math>X \sim exp(0.2)</math><br> | ||
| + | **<math>X \sim exp(1)</math> <br> | ||
| + | **<math>X \sim exp(10)</math> | ||
| − | + | * Locate the maximum density for each one of these distributions. | |
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| + | * Find the height of the density at 3 values of <math>X</math> (one near 0, one near the mean, and one towards the tail of the distribution). | ||
| + | * 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}</math> | ||
| + | * 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}</math> | ||
| + | * Graph and print | ||
| + | ** <math>X \sim N(2,0.5)</math> | ||
| + | ** <math>X \sim N(10,2)</math> | ||
| + | ** <math>X \sim N(20,5)</math> | ||
| + | * Find one percentile for each one of these distributions and locate them on the printouts. | ||
| + | * Find one cumulative probability for each one of these distributions and locate them on the printouts. | ||
| − | + | =='''Exercise 1'''== | |
| + | Construct the joint probability distribution of X and Y. | ||
| − | + | =='''Exercise 2'''== | |
| + | Find the conditional expected value of Y given X=5. | ||
| − | + | =='''Exercise 3'''== | |
| + | Find the conditional variance of Y given X=5. | ||
| − | + | =='''Exercise 4'''== | |
| + | Find the expected value of Y. | ||
| − | + | =='''Exercise 5'''== | |
| + | Find the standard deviation of Y. | ||
| − | + | =='''Exercise 6'''== | |
| + | Graph the probability distribution of Y. | ||
| − | + | =='''Exercise 7'''== | |
| − | + | Use SOCR [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html Experiments] and choose "Die Coin Experiment" to graph and print the empirical distribution of Y when the experiment is performed: | |
| − | + | * n = 1000 times. | |
| − | + | * n= 10000 times | |
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<center>[[Image:SOCR_Activities_DieCoinExperiment_Christou_092206_Fig1.jpg |600px]]</center> | <center>[[Image:SOCR_Activities_DieCoinExperiment_Christou_092206_Fig1.jpg |600px]]</center> | ||
| − | + | =='''Exercise 8'''== | |
| + | Compare the theoretical mean and standard deviation of Y (exercise 4 and 5) with the empirical mean and standard deviation found in exercise 7. | ||
<hr> | <hr> | ||
* 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_ExpDist}} |
Latest revision as of 12:21, 12 June 2007
Contents
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
- Graph and print
- \(X \sim exp(0.2)\)
- \(X \sim exp(1)\)
- \(X \sim exp(10)\)
- \(X \sim exp(0.2)\)
- Locate the maximum density for each one of these distributions.
- 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).
- Find one percentile for each of these distributions and record them on the printouts. Verify these percentiles using the formula we discussed in class\[x_p=\frac{ln(1-\frac{p}{100})}{-\lambda}\]
- Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula\[P(X \le x)=1-e^{-\lambda x}\]
- Graph and print
- \(X \sim N(2,0.5)\)
- \(X \sim N(10,2)\)
- \(X \sim N(20,5)\)
- Find one percentile for each one of these distributions and locate them on the printouts.
- Find one cumulative probability for each one of these distributions and locate them on the printouts.
Exercise 1
Construct the joint probability distribution of X and Y.
Exercise 2
Find the conditional expected value of Y given X=5.
Exercise 3
Find the conditional variance of Y given X=5.
Exercise 4
Find the expected value of Y.
Exercise 5
Find the standard deviation of Y.
Exercise 6
Graph the probability distribution of Y.
Exercise 7
Use SOCR Experiments and choose "Die Coin Experiment" to graph and print the empirical distribution of Y when the experiment is performed:
- n = 1000 times.
- n= 10000 times
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Exercise 8
Compare the theoretical mean and standard deviation of Y (exercise 4 and 5) with the empirical mean and standard deviation found in exercise 7.
- SOCR Home page: http://www.socr.ucla.edu
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