# 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.

• 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.