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Chapter 5: Problem 70

What is the parameter of the Poisson probability distribution, and what does it mean?

Short Answer

Expert verified
The parameter of the Poisson Probability Distribution is \( \lambda \), and it represents the average number of events in a given interval, like time, space or volume. Examples could be the average number of emails received in a day, the average number of phone calls at a call center per hour, etc.

Step by step solution

01

Identifying the Parameter of Poisson Distribution

The parameter of a Poisson distribution is typically denoted by \( \lambda \) (lambda). This a positive rate at which the events are occurring.
02

Meaning of the Parameter

The parameter \( \lambda \) represents the average number of events in an interval. It could be an interval of time, space or volume depending on the context of the experiment being modelled.
03

Examples for better understanding

For instance, if emails are received at a rate of 20 emails per day, then \( \lambda = 20 \) for the Poisson probability distribution modelling the number of emails received in a day.

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Most popular questions from this chapter

Scott offers you the following game: You will roll two fair dice. If the sum of the two numbers obtained is \(2,3,4,9,10,11\), or 12, Scott will pay you \(\$ 20 .\) However, if the sum of the two numbers is \(5,6,7\), or 8 , you will pay Scott \(\$ 20 .\) Scott points out that you have seven winning numbers and only four losing numbers. Is this game fair to you? Should you accept this offer? Support your conclusion with appropriate calculations.

In a 2011 Time/Money Magazine survey of adult Americans, \(61 \%\) said that they were less sure that their children will achieve the American Dream (Time, October 10,2011 ). Suppose that this result is true for the current population of adult Americans. A random sample of 16 adult Americans is selected. Using the binomial probability distribution formula, find the probability that the number of adult Americans in this sample of 16 who hold the above opinion is a. exactly 7 \(\mathbf{b}\), none c. exactly 2

In a group of 20 athletes, 6 have used performance-enhancing drugs that are illegal. Suppose that 2 athletes are randomly selected from this group. Let \(x\) denote the number of athletes in this sample who have used such illegal drugs. Write the probability distribution of \(x\). You may draw a tree diagram and use that to write the probability distribution. (Hint: Note that the selections are made without replacement from a small population. Hence, the probabilities of outcomes do not remain constant for each selection.)

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