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6.2 Exercise 12

Avg difficulty 2.5

The class {A,B,C,D}\left\{A , B , C , D\right\} has minterm probabilities

p m = 0 . 001 * [ 5 7 6 8 9 14 22 33 21 32 50 75 86 129 201 302 ] p m = 0 . 001 \star \left[5 7 6 8 9 14 22 33 21 32 50 75 86 129 201 302\right]
  • Determine whether or not the class is independent.
  • The random variable X=IA+IB+IC+IDX = I_{A} + I_{B} + I_{C} + I_{D} counts the number of the events which occur on a trial. Find the distribution for X and determine the probability that two or more occur on a trial. Find the probability that one or three of these occur on a trial.

Pfeiffer, Applied Probability, 6.2 Problems on Random Variables and Probabilities, exercise 12

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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.