Poisson point distribution

Like with the binomial distribution, the poisson distribution has a formula we can use to calculate the point distribution - the probability of the outcome exactly equalling a certain value.

The formula is:

P(X=x)=\frac{e^{-\lambda}\lambda^x}{x!}

Where:

• P(X=x) is the probability of the outcome exactly equalling x.
• \lambda is the mean number of occurrences in the given interval - or the expectation
• x is the number of occurrences we want to calculate the probability of (e.g. checking the probability of exactly 7 occurences). This must be in the same time frame as the \lambda value!

What does this calculate?

The probability of getting exactly x occurrences in a given interval, given that the average number of occurrences in that interval is \lambda.