The number of clients standing in line at (any) counter in front of you follows a random variable with a Poisson distribution P(5). The waiting time (in minutes, from the moment you joined the line until it's your turn) at each counter is a random variable with an exponential distribution E(1/12). You need to visit 20 counters and receive a form from each to complete administrative tasks. Determine the probabilities: (a) that you will obtain all 20 forms within a maximum of two hours. (b) that while waiting in line at all 20 counters, you will see at least 100 people ahead of you.

The number of clients standing in line at (any) counter in front of you follows a random variable with a Poisson distribution P(5). The waiting time (in minutes, from the moment you joined the line until it's your turn) at each counter is a random variable with an exponential distribution E(1/12). You need to visit 20 counters and receive a form from each to complete administrative tasks. Determine the probabilities: (a) that you will obtain all 20 forms within a maximum of two hours. (b) that while waiting in line at all 20 counters, you will see at least 100 people ahead of you.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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