Question

I'm working on probability HW and working on word problems. Do you have any tips as to how to differentiate between Poisson distributions from Binomials, Geometric and Negative Binomials when doing word problems...i provided an examples for everything but Possion, please explain Poisson distribution using the same example structures

Binomial is simplest one in this we have number of trials given 'n' and probability of success 'p' and they ask for probability of getting success 'r' times.

For example: When we toss a coin 3 times what's probability of getting 2 heads. Here n = 3, p = 0.5 (because success is getting head, and that is 0.5)

Geometric: Geometric is extended form of Binomial distribution almost same just in this it ask for probability of first success in 'r' th trial.

For example: When we toss a coin 3 times what's the probability of getting 1st head on 2nd toss.

Negative binomial: This is one more step ahead it's same as Geometric it ask for 'k' th success in 'r' th trial.

For example: When we toss a coin 3 times what's the probability of getting 2nd head in 3rd toss.

I took same experiment to explain how it change from one distribution to another. I hope this will help.

Answer 1

Here we used to concept of Poisson distribution to see how it is related to Binomial distribution followed by an example in details.
Mothern atiealy a pondom Nariable X is Said to Pollow Poisson distpibution with parameters has the oloutng p 24 Hold on In usords auppose a Bernoulli toial twhere the is pepeated a mo. of imes Suceess s Nery Probabilrhy of The random Naniable Apu. of representing wndep Suceess tollouos Polsspn disth ceptain conditions. obtaimed as Extemtialiu Poisson disto cam lbe a imiting case of Binomial distoibution speaial ease The Poieson distribution is a the Binomial distribution as m the number f trialsgo to infinity while the expeeted number of success remains Rxed as an approximation o5 a is used eshen 'n Binomial (n,p) distribution small. s Nopylarge bot P is Binomial oeeurs for ed set over an triats cohile Poisson seeups te o triais WO.

In Binomial C, eay ond npe Ainite Ahen 4ends Tb Example eoin a biasod uppose se are oersing uth probabili ng a head as 0 O1 ie. P-oopsay 0,000 we ape tossing the eoin tor say Himos then n (no. of triats) 10,000 Here n' is ve large aoopared to Anar the probasti Sueeess. So we use a Poiss on distn in this ease with 0.001 Ao,000 Y 1 IO,00O PEO.001 Probabitity etting heass ie. 10 0.00 227 21

Some other examples of Poisson distribution are:

* Number of accidents in a busy road

* No of misprints in a book.

For any doubts please ask in the comment section.

A ? would be really appreciable.