These distributions are related yet different – here’s a comparison that hopefully clears up any confusions!

Things to know:

• e is Euler’s number – you’ll find e on your calculator or you can use numpy.exp() in Python
• The ‘parameter’ is conventionally written as λ and is pronounced lambda

Poisson	Exponential
Number of events that occur in an interval of time	Time taken between 2 events occurring
For example… the number of Metrorail trains that arrive at the platform in an hour	For example… the time between one Metrorail train arriving and the next
6 trains	10 minutes between trains
The random variable is discrete – this is a countable number of things that happen	The random variable is continuous – typically time, but may represent other factors like distance
λ represents the number of events (per unit of time)	λ represents time between individual events
Graphically, a Poisson distribution looks like this:	Graphically, an Exponential distribution looks like this:
Calculate probability as follows: P(X=x) = e–λλx / x!	Calculate probability as follows: P(x>n) = e-λ(n) P(x<n) = 1 – e-λ(n) P(n<x<m) = P(x<m) – P(x<n)
On average 6 trains arrive at the platform per hour…
What is the probability that fewer than 2 trains arrive in the next 20 minutes?	What is the probability that a train arrives every 8 minutes or less?
λ = 2 per 20 minutes	λ = 0.1 per minute (6/60)
P(X<2) = P(X=0) + P(X=1) = e–220 / 0!  +  e–21/ 1! = 0.41	P(x<8) = 1 – e–0.1(8) = 0.45

2 amazingly simple video tutorials are available on YouTube if you need a quick walk-through:

• Dave Your Tutor
• Wendy Arnold