SOCR EduMaterials Activities CoinDieExperiment - Revision history

IvoDinov: /* Applications - Conditional Probability */

2008-09-12T22:01:38Z

‎Applications - Conditional Probability

IvoDinov: formatting and expansion

2008-09-12T21:58:13Z

formatting and expansion

IvoDinov at 21:53, 12 September 2008

2008-09-12T21:53:12Z

IvoDinov: added the conditional probability as application

2008-09-12T21:51:27Z

added the conditional probability as application

IvoDinov at 03:04, 29 December 2006

2006-12-29T03:04:13Z

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when a coin is tossed first. */

2006-10-20T22:01:42Z

‎This an activity to explore the distribution of the die score (<math> Y </math>) when a coin is tossed first.

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when a coin is tossed first. */

2006-10-20T21:46:48Z

‎This an activity to explore the distribution of the die score (<math> Y </math>) when a coin is tossed first.

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when a coin is tossed first. */

2006-10-20T21:01:49Z

‎This an activity to explore the distribution of the die score (<math> Y </math>) when a coin is tossed first.

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when first a coin is tossed. */

2006-10-20T03:42:44Z

‎This an activity to explore the distribution of the die score (<math> Y </math>) when first a coin is tossed.

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when first a coin is tossed. */

2006-10-20T00:50:49Z

‎This an activity to explore the distribution of the die score (<math> Y </math>) when first a coin is tossed.

@@ Line 20: / Line 20: @@
 *  Reset.  Choose <math> p=0.2 </math>, green fair die, 2-5 flat for red die, perform 100 runs, take a snapshot and comment.
-==Applications - [[AP_Statistics_Curriculum_2007_Prob_Rules#Conditional_Probability | Conditional Probability]]==
+==Applications: [[AP_Statistics_Curriculum_2007_Prob_Rules#Conditional_Probability | Conditional Probability]]==
 The [http://socr.ucla.edu/htmls/exp/Coin_Die_Experiment.html SOCR Coin-Die Experiment] may be used to demonstrate the notion of [[AP_Statistics_Curriculum_2007_Prob_Rules#Conditional_Probability | conditional probability]].

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 == This is an activity to explore the distribution of the die score (<math> Y </math>) when a coin is tossed first.  ==
-Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Coin Die Experiment.  Once you find it, click on the About button and read about the experiment.  Below you can see the outcome of 10 runs of the experiment.
+==Description==
 <center>[[Image: SOCR_Activities_CoinDie_Christou_coindie.jpg|600px]]</center>
 Answer the following questions:
-'''a.'''  There are two random variables (<math> X, \ Y </math>), one parameter (<math> p </math>) for the coin, and the probability distribution that governs each die (green or red) involved in this experiment.  Describe what each one represents.
+* There are two random variables (<math> X, \ Y </math>), one parameter (<math> p </math>) for the coin, and the probability distribution that governs each die (green or red) involved in this experiment.  Describe what each one represents.
-'''b.'''  Choose fair coin (<math> p = 0.5 </math>), and fair dice (green and red).   Perform 100 runs, take a snapshot and comment.
+*  Choose fair coin (<math> p = 0.5 </math>), and fair dice (green and red).   Perform 100 runs, take a snapshot and comment.
-'''c.'''  Reset.  Choose <math> p=0.8 </math>, 1-6 flat for the green die, 3-4 flat for the red die.  Construct the probability distribution of <math> Y </math>, compute the mean of <math> Y </math>, and the standard deviation of <math> Y </math>.  Verify that they agree with the ones in the applet.
+*  Reset.  Choose <math> p=0.8 </math>, 1-6 flat for the green die, 3-4 flat for the red die.  Construct the probability distribution of <math> Y </math>, compute the mean of <math> Y </math>, and the standard deviation of <math> Y </math>.  Verify that they agree with the ones in the applet.
-'''d.'''  Reset.  Choose <math> p=0.2 </math>, green fair die, 2-5 flat for red die, perform 100 runs, take a snapshot and comment.
+*  Reset.  Choose <math> p=0.2 </math>, green fair die, 2-5 flat for red die, perform 100 runs, take a snapshot and comment.
 ==Applications - [[AP_Statistics_Curriculum_2007_Prob_Rules#Conditional_Probability | Conditional Probability]]==

@@ Line 22: / Line 22: @@
 : ''P(A={Coin=H})=23/30''
 : ''P(B={Die-outcome=5})= 3/30 = 1/10''
-: <math>P(A|B) = P(AB)/P(B) = {2/30 \over 3/30} = 20/30 \approx P(A) = 23/30</math>. So, here, independence is controlled by making the two dice have the same probability distributions. Altering the distributions of the 2 dice will introduce a dependence between the events ''A'' and ''B''. Try to validate it by this applet simulation.
+: <math>P(A|B) = {P(AB) \over P(B)} = {2/30 \over 3/30} = 20/30 \approx P(A) = 23/30</math>. So, here, independence is controlled by making the two dice have the same probability distributions. Altering the distributions of the 2 dice will introduce a dependence between the events ''A'' and ''B''. Try to validate it by this applet simulation.
 <hr>
 * SOCR Home page: http://www.socr.ucla.edu
 {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_CoinDieExperiment}}

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 '''d.'''  Reset.  Choose <math> p=0.2 </math>, green fair die, 2-5 flat for red die, perform 100 runs, take a snapshot and comment.
 <hr>
 * SOCR Home page: http://www.socr.ucla.edu
 {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_CoinDieExperiment}}

← Older revision		Revision as of 03:04, 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_ExperimentsActivities~~}}	+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_CoinDieExperiment}}

← Older revision		Revision as of 22:01, 20 October 2006
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−	== This an activity to explore the distribution of the die score (<math> Y </math>) when a coin is tossed first. ==	+	== This is an activity to explore the distribution of the die score (<math> Y </math>) when a coin is tossed first. ==

	Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Coin Die Experiment. Once you find it, click on the About button and read about the experiment. Below you can see the outcome of 10 runs of the experiment.		Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Coin Die Experiment. Once you find it, click on the About button and read about the experiment. Below you can see the outcome of 10 runs of the experiment.

← Older revision		Revision as of 21:01, 20 October 2006
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	'''d.''' Reset. Choose <math> p=0.2 </math>, green fair die, 2-5 flat for red die, perform 100 runs, take a snapshot and comment.		'''d.''' Reset. Choose <math> p=0.2 </math>, green fair die, 2-5 flat for red die, perform 100 runs, take a snapshot and comment.
		+
		+	* SOCR Home page: http://www.socr.ucla.edu
		+
		+	{{translate\|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_ExperimentsActivities}}

← Older revision		Revision as of 03:42, 20 October 2006
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−	== This an activity to explore the distribution of the die score (<math> Y </math>) when ~~first~~ a coin is tossed. ==	+	== This an activity to explore the distribution of the die score (<math> Y </math>) when a coin is tossed first. ==

	Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Coin Die Experiment. Once you find it, click on the About button and read about the experiment. Below you can see the outcome of 10 runs of the experiment.		Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Coin Die Experiment. Once you find it, click on the About button and read about the experiment. Below you can see the outcome of 10 runs of the experiment.

SOCR EduMaterials Activities CoinDieExperiment - Revision history

IvoDinov: /* Applications - Conditional Probability */

IvoDinov: formatting and expansion

IvoDinov at 21:53, 12 September 2008

IvoDinov: added the conditional probability as application

IvoDinov at 03:04, 29 December 2006

Nchristo: /* This an activity to explore the distribution of the die score ( Y ) when a coin is tossed first. */

Nchristo: /* This an activity to explore the distribution of the die score ( Y ) when a coin is tossed first. */

Nchristo: /* This an activity to explore the distribution of the die score ( Y ) when a coin is tossed first. */

Nchristo: /* This an activity to explore the distribution of the die score ( Y ) when first a coin is tossed. */

Nchristo: /* This an activity to explore the distribution of the die score ( Y ) when first a coin is tossed. */

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when a coin is tossed first. */

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when a coin is tossed first. */

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when a coin is tossed first. */

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when first a coin is tossed. */

Nchristo: /* This an activity to explore the distribution of the die score ( $Y$ ) when first a coin is tossed. */