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Statistics / First Course in Probability 8 / Chapter 9 / Problem 9.1

First Course in Probability | 8th Edition | ISBN: 9780136033134 | Authors: Norman S. Nise

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Customers arrive at a bank at a Poisson rate .Suppose that

Chapter 9, Problem 9.1

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QUESTION:

Customers arrive at a bank at a Poisson rate .Suppose that two customers arrived during the firsthour. What is the probability that(a) both arrived during the first 20 minutes?(b) at least one arrived during the first 20 minutes?

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QUESTION:

Customers arrive at a bank at a Poisson rate .Suppose that two customers arrived during the firsthour. What is the probability that(a) both arrived during the first 20 minutes?(b) at least one arrived during the first 20 minutes?

ANSWER:

Problem 9.1

Customers arrive at a bank at a Poisson rate ?. Suppose that two customers arrived during the first hour. What is the probability that

(a) both arrived during the first 20 minutes?

(b) at least one arrived during the first 20 minutes?

Step by Step Solution

Step 1 of 3

Suppose that the two customers arrived during the first hour that is,

So, the probability density function of the Poisson distribution can be defined as,

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