SOCR EduMaterials Activities ExpDist
From Socr
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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] | ||
| - | \begin{itemize} | + | <math>\begin{itemize} |
\item[a.] Graph and print \\ | \item[a.] Graph and print \\ | ||
$X \sim exp(0.2)$ \\ | $X \sim exp(0.2)$ \\ | ||
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\item[1.] Find one percentile for each one of these distributions and locate them on the printouts. | \item[1.] Find one percentile for each one of these distributions and locate them on the printouts. | ||
\item[2.] Find one cumulative probability for each one of these distributions and locate them on the printouts. | \item[2.] Find one cumulative probability for each one of these distributions and locate them on the printouts. | ||
| - | \end{itemize} | + | \end{itemize}</math> |
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| - | + | =='''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: | ||
a. n = 1000 times. | a. n = 1000 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}} |
Revision as of 17:10, 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
Failed to parse (unknown function\begin): \begin{itemize} \item[a.] Graph and print \\ $X \sim exp(0.2)$ \\ $X \sim exp(1)$ \\ $X \sim exp(10)$ \begin{itemize} \item[1.] Locate the maximum density for each one of these distributions. \item[2.] 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). \item[3.] Find one percentile for each of these distributions and record them on the printouts. Verify these percentiles using the formula we discussed in class: \[ x_p=\frac{ln(1-\frac{p}{100})}{-\lambda} \] \item[4.] Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula: \[ P(X \le x)=1-e^{-\lambda x} \] \end{itemize} \item[b.] Graph and print \\ $X \sim N(2,0.5)$ \\ $X \sim N(10,2)$ \\ $X \sim N(20,5$ \begin{itemize} \item[1.] Find one percentile for each one of these distributions and locate them on the printouts. \item[2.] Find one cumulative probability for each one of these distributions and locate them on the printouts. \end{itemize}
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:
a. n = 1000 times.
b. n= 10000 times
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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