SOCR EduMaterials Activities ExpDist - Revision history

IvoDinov at 17:21, 12 June 2007

2007-06-12T17:21:57Z

IvoDinov at 17:20, 12 June 2007

2007-06-12T17:20:24Z

IvoDinov at 17:16, 12 June 2007

2007-06-12T17:16:07Z

Nchristo at 00:52, 24 September 2006

2006-09-24T00:52:22Z

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 14: / Line 14: @@
 * 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:
+* 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:
+* 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

@@ Line 5: / Line 5: @@
 You can access the applet for the [http://www.socr.ucla.edu/htmls/SOCR_Distributions.html Exponential Distributions]
-<math>\begin{itemize}
+* Locate the maximum density for each one of these distributions.
 =='''Exercise 1'''==
@@ Line 64: / Line 55: @@
 =='''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.
-a. n = 1000 times.
+* n= 10000 times
 <center>[[Image:SOCR_Activities_DieCoinExperiment_Christou_092206_Fig1.jpg |600px]]</center>

@@ Line 1: / Line 1: @@
-== 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]
+=='''Description'''==
-\begin{itemize}
+<math>\begin{itemize}
 \item[a.] Graph and print \\
 $X \sim exp(0.2)$ \\
@@ Line 29: / Line 30: @@
 \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}
+\end{itemize}</math>
@@ Line 37: / Line 38: @@
-* '''Exercise 1''': Construct the joint probability distribution of X and Y.
+=='''Exercise 1'''==
-* '''Exercise 2''': Find the conditional expected value of Y given X=5.
+=='''Exercise 2'''==
-* '''Exercise 3''': Find the conditional variance of Y given X=5.
+=='''Exercise 3'''==
-* '''Exercise 4''':  Find the expected value of Y.
+=='''Exercise 4'''==
-* '''Exercise 5''': Find the standard deviation of Y.
+=='''Exercise 5'''==
-* '''Exercise 6''': Graph the probability distribution of Y.
+=='''Exercise 6'''==
-* '''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:
+=='''Exercise 7'''==
 a. n = 1000 times.
@@ Line 63: / Line 71: @@
 <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.
+=='''Exercise 8'''==
 <hr>
 * 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_ExpDist}}