# Difference between revisions of "SOCR EduMaterials Activities DieCoin"

(→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.) |
||

Line 5: | Line 5: | ||

* '''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. | ||

− | * '''Exercise 1''': | + | * '''Exercise 1''': Construct the joint probability distribution of X and Y. |

− | + | * '''Exercise 2''': Find the conditional expected value of Y given X=5. | |

− | |||

− | * '''Exercise | + | * '''Exercise 3''': Find the conditional variance of Y given X=5. |

− | |||

− | |||

− | + | * '''Exercise 4''': Find the expected value of Y. | |

− | * '''Exercise | + | * '''Exercise 5''': Find the standard deviation of Y. |

− | |||

− | |||

− | + | * '''Exercise 6''': Graph the probability distribution of Y. | |

+ | |||

+ | * '''Exercise 7''': Use SOCR [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html] and choose "Die Coin Experiment" to graph and print the empirical distribution of Y when the experiment is performed: | ||

+ | |||

+ | * '''Exercise 8''': Find the conditional variance of Y given X=5. | ||

<hr> | <hr> |

## Revision as of 18:42, 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 [1] and choose "Die Coin Experiment" to graph and print the empirical distribution of Y when the experiment is performed:

**Exercise 8**: Find the conditional variance of Y given X=5.

- SOCR Home page: http://www.socr.ucla.edu

Translate this page: