AS level
Stats
S1

AS level Stats S1
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Poisson Distribution
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A Revision Guide


A theoretical distribution
It is a good approximation to the binomial distribution
Used when you have low probability and high number of trials
characteristics

Very similar to binomial but with a large sample and small probability

 Fixed number of trials (n) and in excess of 50

Constant Probability (p) typically 0.1 or less

only two possible outcomes (yes/no, true/false etc)

Independent trials

Manual Calculation.
In these calculations we use a new Greek character λ (Lamda)

The formula for calculation the probability of exactly x occurences
over a timespan of λ is
P(x;λ) = λxe-λ / x!
NOTE : ex is a special function on your calculator

Example
The number of letters arriving at an office per day is assumed to have a Poisson distribution with mean 6.3. Find the probability that the number of letters arriving on a randomly chosen day is
a) exactly 5
So we expect to get 6.3 letters per day
but want to know the probability of only getting exactly 5 in ONE day
so λ = 6.3 (per day) x 1 (ONE day) = 6.3
and x = 5

P(x;λ) = λxe-λ / x!
P(5;6.3) = 6.35e-6.3 / 5!
=
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b) less than 3
this means that we need to do - P(less than 3) = P(0) + P(1) + P(2)
notes
"Distribution" is the way in which the data is arranged. It's characteristics affect the way that we must deal with it.

"Poisson" has nothing to do with fish. Ask monsieur Poisson.
website by LJ Middleton
www.lawrencejohn.net