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15.3 Exercise 25

Avg difficulty 2.5

The number of customers during the noon hour at a bank teller's station is a random number N with distribution

N = 1 : 10 , P N = 0 . 01 * [ 5 7 10 11 12 13 12 11 10 9 ] N = 1 : 10 , P N = 0 . 01 \star \left[5 7 10 11 12 13 12 11 10 9\right]

The amounts they want to withdraw can be represented by an iid class having the common distribution Y∼Y \sim exponential (0.01). Determine the probabilities that the maximum withdrawal is less than or equal to t for t=100,200,300,400,500t = 100 , 200 , 300 , 400 , 500.

Pfeiffer, Applied Probability, 15.3 Problems on Random Selection, exercise 25

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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.