Related yet different, here’s how…
A quick note on the “preliminary terrors” of notation:
- e is Euler’s number – you’ll find the e on your calculator or the EXP() function in Excel
- The parameter is conventionally written as λ (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 |
| l represents the number of events (per unit of time) | l represents time between individual events |
| Graphically, a Poisson distribution looks like this:
|
Graphically, an Exponential distribution looks like this:
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| 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) |
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On average 6 trains arrive at the platform per hour… |
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| 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:
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