The number of views of a page on a Web site follows a...

Name: Problem 170, Chapter 3: Applied Statistics and Probability for Engineers
Uploaded: 2021-08-10T18:47:02-08:00
Duration: 2 min 10 s
Channel: Maxime Rossetti
Description: The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. (a) What is the probability of no views in a minute? (b) What is the probability of two or fewer views in 10 minutes? (c) Does the answer to the previous part depend on whether the 10-minute period is an uninterrupted interval? Explain.

The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. (a) What is the probability of no views in a minute? (b) What is the probability of two or fewer views in 10 minutes? (c) Does the answer to the previous part depend on whether the 10-minute period is an uninterrupted interval? Explain.

The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute.
(a) What is the probability of no views in a minute?
(b) What is the probability of two or fewer views in 10 minutes?
(c) Does the answer to the previous part depend on whether the 10-minute period is an uninterrupted interval? Explain.

Key Concepts

Poisson Distribution

The Poisson distribution is a probability distribution that describes the number of events occurring in a fixed interval of time or space, given that these events occur with a known constant mean rate and independently of the time since the last event. It is widely used to model count-based phenomena in various fields such as physics, finance, and traffic engineering.

Probability Mass Function

The probability mass function (PMF) for a Poisson random variable gives the probability that the variable takes a specific discrete value. It is expressed as P(X = k) = (?^k e^(-?)) / k! where ? is the average number of events in the interval, k is the number of events, and e is the base of the natural logarithm. This function is crucial for computing the likelihood of any given number of events within the specified period.

Time Scaling in Poisson Processes

Time scaling in Poisson processes refers to the property that the number of events in a longer interval can be modeled as a Poisson distribution with a rate equal to the original rate multiplied by the length of the interval. This property simplifies calculation over different time periods, as the overall distribution over any interval is still Poisson, with its mean adjusted for the length of the interval.

Independence of Increments

The independence of increments is a key concept in Poisson processes, which posits that the number of events occurring in non-overlapping intervals are independent of each other. This property implies that splitting an interval into several segments does not affect the distribution of events in the overall interval, thus ensuring that computations remain consistent regardless of whether the time period is viewed as a single continuous interval or partitioned into separate parts.

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