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Chapter 5: Problem 48

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 (\(\lambda\)) which is the average rate at which the events occur in a fixed interval.

Step by step solution

01

Definition of Poisson Distribution

The Poisson distribution is a mathematical concept used in statistics and is used for describing the distribution of rare events in a large population. It is a discrete probability distribution expressing the probability of a given number of events occurring in a fixed interval of time or space.
02

Understanding the Parameter (Lambda)

The parameter of the Poisson distribution is commonly denoted as lambda (\(\lambda\)). This parameter represents the average rate at which events occur over a certain period of time or space. In other words, \(\lambda\) is the expected number of occurrences in a given interval.
03

The Meaning of the Parameter (Lambda)

\(\lambda\) or lambda, indicates the rate of occurrences of an event per unit of time or space. For instance, if a call center receives 12 calls per hour on average, the lambda of the associated Poisson distribution would be 12. In other words, the Poisson parameter, \(\lambda\), corresponds to the mean or average value of the distribution.

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Most popular questions from this chapter

According to a survey, \(18 \%\) of the car owners said that they get the maintenance service done on their cars according to the schedule recommended by the auto company. Suppose that this result is true for the current population of car owners. a. Let \(x\) be a binomial random variable that denotes the number of car owners in a random sample of 12 who get the maintenance service done on their cars according to the schedule recommended by the auto company. What are the possible values that \(x\) can assume? b. Find the probability that exactly 3 car owners in a random sample of 12 get the maintenance service done on their cars according to the schedule recommended by the auto company. Use the binomial probability distribution formula.

Explain the hypergeometric probability distribution. Under what conditions is this probability distribution applied to find the probability of a discrete random variable \(x\) ? Give one example of an application of the hypergeometric probability distribution.

Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company's management. The company guarantees a refund or a replacement for any calculator that malfunctions within 2 years from the date of purchase. It is known from past data that despite all efforts, \(5 \%\) of the calculators manufactured by the company malfunction within a 2-year period. The company mailed a package of 10 randomly selected calculators to a store. a. Let \(x\) denote the number of calculators in this package of 10 that will be returned for refund or replacement within a 2 -year period. Using the binomial probabilities table, obtain the probability distribution of \(x\) and draw a histogram of the probability distribution. Determine the mean and standard deviation of \(x\). b. Using the probability distribution of part a, find the probability that exactly 2 of the 10 calculators will be returned for refund or replacement within a 2 -year period.

Which of the following are binomial experiments? Explain why. a. Rolling a die 10 times and observing the number of spots b. Rolling a die 12 times and observing whether the number obtained is even or odd c. Selecting a few voters from a very large population of voters and observing whether or not each of them favors a certain proposition in an election when \(54 \%\) of all voters are known to be in favor of this proposition.

Briefly explain the following. a. A binomial experiment b. A trial c. A binomial random variable
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