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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* '''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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             *n = 1000 times
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             a. n = 1000 times
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             *n= 10000 times
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             b. n= 10000 times
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* '''Exercise 8''': Compare the theoretical mean and standard deviation of $Y$ (parts (d) and (e)) with the empirical mean and standard deviation found in part 7.
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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.
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Revision as of 22:44, 23 September 2006

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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