# SOCR EduMaterials Activities DieCoin

## 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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