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Back to 15.3 Problems on Random Selection

15.3 Exercise 9

Avg difficulty 2.5

A supply house stocks seven popular items. The table below shows the values of the items and the probability of each being selected by a customer.

Value 12.50 25.00 30.50 40.00 42.50 50.00 60.00
Probability 0.10 0.15 0.20 0.20 0.15 0.10 0.10

Suppose the purchases of customers are iid, and the number of customers in a day is binomial (10,0.5). Determine the distribution for the total demand D.

  1. How many different possible values are there? What is the maximum possible total sales?
  2. Determine E[D]E \left[D\right] and P(D≤t)P \left(D \leq t\right) for t=100,150,200,250,300t = 100 , 150 , 200 , 250 , 300.
    Determine P(100<D≤200)P \left(100 < D \leq 200\right).

Pfeiffer, Applied Probability, 15.3 Problems on Random Selection, exercise 9

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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.