SOCR EduMaterials Activities DieCoin

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(This is an activity to explore the bivariate distribution of X and Y where X is the number shown when a die is rolled and Y is the number of heads when a coin is tossed number of times equal to X.)
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== This is an activity to explore the bivariate distribution of X and Y where X is the number shown when a die is rolled and Y is the number of heads when a coin is tossed number of times equal to X. ==
== This is an activity to explore the bivariate distribution of X and Y where X is the number shown when a die is rolled and Y is the number of heads when a coin is tossed number of times equal to X. ==
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* '''Description''': A die is rolled and the number observed X is recorded.  Then a coin is tossed number of times equal to the value of X.  For example if X=2 then the coin is tossed twice, etc.  Let Y be the number of heads observed.  Note:  Assume that the die and the coin are fair.
* '''Description''': A die is rolled and the number observed X is recorded.  Then a coin is tossed number of times equal to the value of X.  For example if X=2 then the coin is tossed twice, etc.  Let Y be the number of heads observed.  Note:  Assume that the die and the coin are fair.
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b. n= 10000 times
b. n= 10000 times
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<center>[[Image:SOCR_Activities_DieCoinExperiment_Christou_092206_Fig1.jpg |300px]]</center>
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<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''': Compare the theoretical mean and standard deviation of Y (exercise 4 and 5) with the empirical mean and standard deviation found in exercise 7.
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* SOCR Home page: http://www.socr.ucla.edu
* SOCR Home page: http://www.socr.ucla.edu
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{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_ConfidenceIntervals}}
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{{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_DieCoin}}

Current revision as of 15:40, 17 September 2007

SOCR Educational Materials - Activities - SOCR Die Coin Activity

This is an activity to explore the bivariate distribution of X and Y where X is the number shown when a die is rolled and Y is the number of heads when a coin is tossed number of times equal to X.

  • Description: A die is rolled and the number observed X is recorded. Then a coin is tossed number of times equal to the value of X. For example if X=2 then the coin is tossed twice, etc. Let Y be the number of heads observed. Note: Assume that the die and the coin are fair.


  • 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.



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