• No products in the cart.

# POISSON DISTRIBUTION

• #### For example, the average number of visitors coming on a website in a day are 1000 but the number of visitors between 11 am, and 2 pm not known.

Probability mass function or of x events occurring in an interval –

P(x) = (λx e-λ )/x!

e – Euler’s number – 2.718

E(X) = µ – Mean expected value

µ = λ = No. of time event occurs / Interval

Example – Number of visitors coming on the website in 1 hour or a number of Ford SUVs between New Jersey and New York.

Probability of occurrence is –

P(x) = (λx e-λ )/x!

e – Euler’s number – 2.718

λ – Average Value A cumulative mass function is the sum of all discrete probabilities –

The probability of viewing fewer than 10 events in Poisson Distribution is :

P(X, x <10) = ∑9i=0 (λx e-λ )/x!

(λ0 e-λ )/0! + (λ1 e-λ )/1!+ ….

Then probabilities of seeing at least one is

1 – the probability of occurrences none.

P(X, x >=1) = 1 – P(X:x=0)

1 – (λ0 e-λ )/0! = 1 – e-λ

• #### If you know the expected value λ over an hour, then the expected value over 1 minute of that hour is – λminute = λ hour/60

A quick exercise in understanding it better

A store sells on average 10 mobile phones in a week.

3. #### What is the probability of the store of not selling any phone on coming Tuesday? August 16, 2019