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Poisson distribution with examples and answers
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a note on Poisson distribution. how to calculate it in excel, python and R
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Understanding the concept of Poisson distribution and how to practice it using excel, R andpython
Poisson distribution
Poisson distribution is a statistical distribution model that can predict the probability of an
event occurring at a given condition (space or time).
Is used for discrete data or events per an instance such as a period of time, batch etc.
hence the Poisson distribution model can be employed to predict the;
• number of events occurring within a given time interval.
• number of errors by employee making count or entering data per week
• arrival of new buy or sell orders entered into an online store
• expected arrival of orders at trading platform
• appearance of a bug in a software
• issuing of red or yellow card in a football match
• Death by a disease
• Machine malfunctions per year or work shit
• Website or hospital visitors per week or per season
• War cases per year
To use the Poisson distribution model, normally one should have data and find the mean
of the taken data (that is all needed from the data to find the probability of the event
happening per time or space).
here:
X is a random variable following a Poisson distribution
k is the number of times an event occurs
P(X = k) is the probability that an event will occur k times
e is Euler’s constant (approximately 2.718)
\lambda is the average number of times an event occurs
! is the factorial function
Practical examples using formula, R software, python and excel
1. Using formula
An average of 5 cards are shown in a laliga football game. calculate the probability that 3
cards will be shown in an upcoming top fixture over the weekend.
e = 2.718
P(x=3) =[(2.718^-5 )*(5^3)]/3!
0.1403739
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