SOCR EduMaterials Activities JointDistributions - Revision history

IvoDinov at 03:12, 29 December 2006

2006-12-29T03:12:05Z

Nchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */

2006-11-25T05:25:30Z

‎This is an activity to explore the joint distributions of X and Y through two simple examples.

Nchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */

2006-11-25T05:20:01Z

‎This is an activity to explore the joint distributions of X and Y through two simple examples.

Nchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */

2006-11-25T05:19:18Z

‎This is an activity to explore the joint distributions of X and Y through two simple examples.

Nchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */

2006-11-25T05:18:08Z

‎This is an activity to explore the joint distributions of X and Y through two simple examples.

Nchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */

2006-11-25T05:17:34Z

‎This is an activity to explore the joint distributions of X and Y through two simple examples.

Nchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */

2006-11-25T05:14:45Z

‎This is an activity to explore the joint distributions of X and Y through two simple examples.

Nchristo: /* This is an activity to explore the joint distributions of X and Y through two simple examples. */

2006-11-25T05:14:20Z

‎This is an activity to explore the joint distributions of X and Y through two simple examples.

Nchristo: /* This is an activity to explore he joint distributions of X and Y through two simple examples. */

2006-11-25T05:12:54Z

‎This is an activity to explore he joint distributions of X and Y through two simple examples.

Nchristo at 05:11, 25 November 2006

2006-11-25T05:11:59Z

New page

== This is an activity to explore he joint distributions of X and Y through two simple examples. ==

You can access the following experiments in SOCR under Experiments.

* '''Exercise 1''': Die coin experiment:
A die is rolled and the number observed <math> X </math> is recorded. Then a coin is tossed number of times equal to the value of <math>X</math?. For example if <math>X=2</math> then the coin is tossed twice, etc. Let <math>Y</math> be the number of heads observed. Note: Assume that the die and the coin are fair.
**'''1.''' Construct the joint probability distribution of <math>X</math> and <math>Y</math>.
**'''2.''' Find the conditional expected value of <math>Y</math> given <math>X=5</math>.
**'''3.''' Find the conditional variance of <math>Y</math> given <math>X=5</math>.
**'''4.''' Find the expected value of <math>Y</math>.
**'''5.''' Find the standard deviation of <math>Y</math>.
**'''6.''' Graph the probability distribution of <math>Y</math>.
**'''7.''' Use SOCR to graph and print the empirical distribution of <math>Y</math> when the experiment is performed
***'''a.''' <math>n=1000</math> times.
***'''b.''' <math>n=10000</math> times.

**'''8.''' Compare the theoretical mean and standard deviation of <math>Y</math> (parts (4) and (5)) with the empirical mean and standard deviation found in part (8).

Below you can see a snapshot of the theoretical distribution of <math> Y </math>.

* '''Exercise 2''': Coin Die experiment:
A coin is tossed and if heads is observed then a red die is rolled. If tails is observed then a green die is rolled. You can choose the distribution of each die as well as the probability of heads. Choose for the red die the 3-4 flat distribution and for the green die the skewed right distribution. Finally using the scroll button choose $p=0.2$ as the probability of heads. Let <math>X</math> be the score of the coin (1 for heads, 0 for tails), and let <math>Y</math> be the score of the die (1,2,3,4,5,6).
**'''1.''' Construct the joint probability distribution of <math>X, Y</math>.
**'''2.''' Find the marginal probability distribution of <math>Y</math> and verify that it is the same with the one given in the applet.
**'''3.''' Compute <math>E(Y)</math>.
**'''4.''' Compute <math>E(Y)</math> using expectation by conditioning <math>E[E(Y|X)]</math>.
**'''5.''' Run the experiment 1000 times take a snapshot and comment on the results.

Below you can see a snapshot of the theoretical distribution of <math> Y </math>.

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

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

← Older revision		Revision as of 03:12, 29 December 2006
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	* 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_JointDistributions}}

← Older revision		Revision as of 05:25, 25 November 2006
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	Below you can see a snapshot of the theoretical distribution of <math> Y </math>.		Below you can see a snapshot of the theoretical distribution of <math> Y </math>.

		+	<center>[[Image: SOCR_Activities_Christou_christou_diecoin.jpg\|600px]]</center>


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	Below you can see a snapshot of the theoretical distribution of <math> Y </math>.		Below you can see a snapshot of the theoretical distribution of <math> Y </math>.

		+	<center>[[Image: SOCR_Activities_Christou_christou_coindie.jpg\|600px]]</center>

@@ Line 1: / Line 1: @@
 == This is an activity to explore the joint distributions of X and Y through two simple examples. ==
-* '''Description''':  You can access the applets for the folowing experiments at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments]
+* '''Description''':  You can access the applets for the following experiments at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments]
 * '''Exercise 1''':  Die coin experiment:

@@ Line 1: / Line 1: @@
 == This is an activity to explore the joint distributions of X and Y through two simple examples. ==
-* '''Description''':  You can access the applets for the folowing experiments at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html Exponential Distributions]
+* '''Description''':  You can access the applets for the folowing experiments at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments]
 * '''Exercise 1''':  Die coin experiment:

@@ Line 1: / Line 1: @@
 == This is an activity to explore the joint distributions of X and Y through two simple examples. ==
-You can access the following experiments in SOCR under Experiments.
+* '''Description''':  You can access the applets for the folowing experiments at [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html Exponential Distributions]
 * '''Exercise 1''':  Die coin experiment:

@@ Line 4: / Line 4: @@
 * '''Exercise 1''':  Die coin experiment:
-A die is rolled and the number observed <math> X </math> is recorded.  Then a coin is tossed number of times equal to the value of <math>X</math?.  For example if <math>X=2</math> then the coin is tossed twice, etc.  Let <math>Y</math> be the number of heads observed.  Note:  Assume that the die and the coin are fair.
+A die is rolled and the number observed <math> X </math> is recorded.  Then a coin is tossed number of times equal to the value of <math>X</math>.  For example if <math>X=2</math> then the coin is tossed twice, etc.  Let <math>Y</math> be the number of heads observed.  Note:  Assume that the die and the coin are fair.
 **'''1.''' Construct the joint probability distribution of <math>X</math> and <math>Y</math>.
 **'''2.'''  Find the conditional expected value of <math>Y</math> given <math>X=5</math>.

← Older revision		Revision as of 05:14, 25 November 2006
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	{{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_ConfidenceIntervals}}
−
−	~~</math>~~

← Older revision		Revision as of 05:14, 25 November 2006
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	* 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~~}	+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfidenceIntervals}}
		+
		+	</math>

← Older revision		Revision as of 05:12, 25 November 2006
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−	== This is an activity to explore he joint distributions of X and Y through two simple examples. ==	+	== This is an activity to explore the joint distributions of X and Y through two simple examples. ==

	You can access the following experiments in SOCR under Experiments.		You can access the following experiments in SOCR under Experiments.