Named After SiméonDenis Poisson Whats The Big Deal Binomial and Geometric distributions only work when we have Bernoulli trials There are three conditions for those They happen often enough to be sure but a good many situations do not fit those models ID: 445586 Download Presentation

The Poisson random variable was first introduced by the French mathematician Simeon-Denis Poisson (1781-1840). He discovered it as a limit to the binomial distribution as the number of trials . n. approaches infinity..

. and Exponential Distributions. 5. Introduction. Several specific distributions commonly occur in a variety of business situations:. N. ormal distribution—a continuous distribution . characterized .

. and Exponential Distributions. 5. Introduction. Several specific distributions commonly occur in a variety of business situations:. N. ormal distribution—a continuous distribution . characterized .

satellite to track carbon dioxide in the . Earth. ’s atmosphere failed to reach its orbit during launching Tuesday morning, scuttling the $278 million mission.. . Andrew Lee/U.S. Air Force, via Associated Press.

The Geometric and Poisson Distributions Geometric Distribution – A geometric distribution shows the number of trials needed until a success is achieved. Example: When shooting baskets, what is the probability that the first time you make the basket will be the fourth time you shoot the ball?

for . Dispersed Count . Data. Kimberly F. Sellers, Ph.D.. Department of Mathematics and Statistics. Georgetown University . Presentation Outline. Background distributions and properties. Poisson distribution.

for . Dispersed Count . Data. Kimberly F. Sellers, Ph.D.. Department of Mathematics and Statistics. Georgetown University . Presentation Outline. Background distributions and properties. Poisson distribution.

That is the table gives Xx 01 02 03 04 05 06 07 08 09 10 12 14 16 18 x 09048 08187 07408 06703 06065 05488 04966 04493 04066 03679 03012 02466 02019 01653 09953 09825 09631 09384 09098 08781 08442 08088 07725 07358 06626 05918 05249 04628 09998 09

Quantitative Analysis for Business Decisions. 2. 4.6 Standard Discrete Distributions continued. Further Examples on Use. Example 5. : . The probability of a . good. component in inspecting assembly line output is known to be 0.8 ; probability of a .

. . . Summary from last time. Discrete Random Variables. Binomial distribution . . – number . of successes from . independent Bernoulli (YES/NO) trials. . . Standard deviation . – measure spread of distribution.

Named After Siméon-Denis Poisson. What’s The Big Deal?. Binomial and Geometric distributions only work when we have Bernoulli trials.. There are three conditions for those.. They happen often enough, to be sure, but a good many situations do not fit those models..

Embed :

Presentation Download Link

Download Presentation - The PPT/PDF document "Poisson Distribution" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.

Slide1

Poisson Distribution

Named After Siméon-Denis PoissonSlide2

What’s The Big Deal?

Binomial and Geometric distributions only work when we have Bernoulli trials.

There are three conditions for those.

They happen often enough, to be sure, but a good many situations do not fit those models.

The Poisson Distribution works in a slightly different situation, but different enough that the situations we can describe just shoots through the roof.Slide3

Poisson Distribution

The Poisson distribution is used when we have a discrete random variable and all we know is the following two things:

The average count in a certain timeframe.

That the amount of time it takes the event to happen again is independent.

I think some examples will really clear this up.Slide4

Poisson Distribution Examples

If you know the average number of car wrecks per week/month/year for a specific intersection (or stretch of highway), then it is Poisson.

If you know the average number of defective units produced on an assembly line per hour, then it is Poisson.

If you know the average number of children born in Pocatello, ID each day, then it is Poisson.Slide5

Poisson Distribution Examples

Wikipedia cites some examples in the real world.

The number of soldiers killed by horse-kicks each year in each corps in the Prussian cavalry.

The number of phone calls at a call centre per minute.

Under an assumption of homogeneity, the number of times a web server is accessed per minute.

The number of mutations in a given stretch of DNA after a certain amount of radiation.

The proportion of cells that will be infected at a given multiplicity of infection.Slide6

Poisson Distribution

The math for this involves e (as in the base of the natural log) and involves the factorial (those really excited numbers we talked about yesterday).

The actual formula will only be discussed on Special Topics day, thanks to our calculator.

poissonpdf

will be used to find the probability of a specific number of occurrences.

poissoncdf

will be used to find the probability that anything from 0 to a specific number of occurrences has happened.Slide7

Poisson Distribution

A Poisson distribution is only defined by the mean. In other words, once we know the mean, we have the Poisson distribution.

The Greek letter we use for this is lambda.

It kind of looks like an upside down lowercase y.

Lambda ->

λ

Again, this is the mean of the Poisson distribution, instead of our old standby

μ

.Slide8

Poisson Distribution

The variance of the Poisson distribution is actually also

λ

.

Which means that the standard deviation of a Poisson distribution is the square root of

λ

.

What this really means is that when you add two Poisson distributions together, you can just add the

λ

values to find the new one.Slide9

Poisson Distribution

What this means is that if a particular intersection averages 2.3 wrecks a month, then it averages 27.6 wrecks a year, and we can just use either figure.

If we know the average per week, we just divide by 7, and booyah…daily average.

So if we know what timeframe the average is for, we can multiply and divide it as necessary to get the one we want.

This only works with Poisson.

© 2021 docslides.com Inc.

All rights reserved.