SOCR EduMaterials Activities Exponential Distribution - Revision history

Rgidwani at 19:01, 8 July 2007

2007-07-08T19:01:21Z

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

2007-07-06T23:06:13Z

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

IvoDinov at 00:41, 29 December 2006

2006-12-29T00:41:55Z

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

2006-09-26T00:20:41Z

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

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

2006-09-24T01:18:04Z

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

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

2006-09-24T01:10:22Z

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

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

2006-09-24T01:03:16Z

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

Nchristo at 00:54, 24 September 2006

2006-09-24T00:54:56Z

New page

== 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}
\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 [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.

b. n= 10000 times

<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>
* SOCR Home page: http://www.socr.ucla.edu

{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfidenceIntervals}}

@@ Line 10: / Line 10: @@
 * '''Exercise 1:''' Graph and print:
-a. exp(0.2)
+**a. exp(0.2)
+**b. exp(1)
-b. exp(1)
+**c. exp(10)
 * '''Exercise 2:''' Locate the maximum density for each one of these distributions.

@@ Line 4: / Line 4: @@
 * '''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>

← Older revision		Revision as of 00:41, 29 December 2006
Line 37:		Line 37:
	* 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=~~SOCR_EduMaterials_Activities_ConfidenceIntervals~~}}	+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_Exponential_Distribution}}

@@ Line 21: / Line 21: @@
 * '''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:
-\[
 x_p=\frac{ln(1-\frac{p}{100})}{-\lambda}
-\]
+</math>
 * '''Exercise 5:''' Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula:
-\[
+<math>
 P(X \le x)=1-e^{-\lambda x}
-\]
+</math>

@@ Line 11: / Line 11: @@
 * '''Exercise 1:''' Graph and print:
 a. exp(0.2)
 b. exp(1)
 c. exp(10)

← Older revision		Revision as of 01:10, 24 September 2006
Line 6:		Line 6:
	* 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_DieCoinExperiment_Christou_092206_Fig1~~.jpg \|600px]]</center>	+	<center>[[Image:SOCR_Activities_ExponentialDistribution_Christou_092206_Fig1.jpg \|600px]]</center>

@@ Line 4: / Line 4: @@
 * '''Description''':  You can access the applet for the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html Exponential Distributions]
-\begin{itemize}
+<center>[[Image:SOCR_Activities_DieCoinExperiment_Christou_092206_Fig1.jpg |600px]]</center>
-\item[a.] Graph and print \\
-$X \sim exp(0.2)$ \\
-$X \sim exp(1)$ \\
+* '''Exercise 1:''' Graph and print:
-$X \sim exp(10)$
+a. exp(0.2)
-\begin{itemize}
+b. exp(1)
-\item[1.] Locate the maximum density for each one of these distributions.
+c. exp(10)
-\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:
+* '''Exercise 2:''' Locate the maximum density for each one of these distributions.
 \[
 x_p=\frac{ln(1-\frac{p}{100})}{-\lambda}
 \]
-\item[4.] Compute one cumulative probability for each one of these distributions, show it on the graph, and verify it with the formula:
 \[
 P(X \le x)=1-e^{-\lambda x}
 \]
 <hr>