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Back to 8.3 Problems On Random Vectors and Joint Distributions

8.3 Exercise 5

Avg difficulty 2.5

Suppose a pair of dice is rolled. Let X be the total number of spots which turn up. Roll the pair an additional X times. Let Y be the number of sevens that are thrown on the X rolls. Determine the joint distribution for the pair {X,Y}\left\{X , Y\right\} and from this determine the marginal distribution for Y. What is the probability of three or more sevens?

Pfeiffer, Applied Probability, 8.3 Problems On Random Vectors and Joint Distributions, exercise 5

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.