The time between incoming calls to a help desk can be seen as a Poisson distributed random variable with an average of three minutes, and the duration can be seen as a discrete random variable. The following tables show a cumulative distribution of incoming calls (made from a Poisson distribution) and the duration of each call, respectively:

Generate a Monte Carlo simulation for the first 10 calls arriving. What is the approximate waiting time for one customer, and how long will all 10 calls take? What is the average duration of each call?

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INC. CAL. PROBABILITY DURATION PROBABILITY 0 0.05 1 0.15 2 0.07 2 3 4 0.23 0.22 0.18 3 0.35 4 0.31 5 0.20 5 6 0.11 0.06 6 0.07