Difference between revisions of "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. == | == 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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* '''Exercise 1''': Construct the joint probability distribution of X and Y. | * '''Exercise 1''': Construct the joint probability distribution of X and Y. | ||
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* '''Exercise 2''': Find the conditional expected value of Y given X=5. | * '''Exercise 2''': Find the conditional expected value of Y given X=5. | ||
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* '''Exercise 3''': Find the conditional variance of Y given X=5. | * '''Exercise 3''': Find the conditional variance of Y given X=5. | ||
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* '''Exercise 4''': Find the expected value of Y. | * '''Exercise 4''': Find the expected value of Y. | ||
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* '''Exercise 5''': Find the standard deviation of Y. | * '''Exercise 5''': Find the standard deviation of Y. | ||
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* '''Exercise 6''': Graph the probability distribution of Y. | * '''Exercise 6''': Graph the probability distribution of Y. | ||
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* '''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''': 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: | ||
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| − | + | a. n = 1000 times. | |
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| + | b. n= 10000 times | ||
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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 | ||
| − | {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title= | + | {{translate|pageName=http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_DieCoin}} |
Latest revision as of 10:46, 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
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- 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.
- SOCR Home page: http://www.socr.ucla.edu
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