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.

Question	Answer
P(X=x)=\frac{e^{-\lambda}\lambda^x}{x!}	The formula for the Poisson point distribution, where P(X=x) is the probability of exactly x occurrences, \lambda is the mean number of occurrences in the interval, and x is the number of occurrences to calculate the probability for.
What does x represent in the Poisson distribution?	The number of occurrences we want to calculate the probability of (e.g., 7). It must be in the same time frame as \lambda.
What is \lambda in the Poisson distribution?	The mean number of occurrences in the given interval, also known as the expectation.
What does the Poisson point distribution calculate?	The probability of getting exactly x occurrences in a given interval, given that the average number of occurrences in that interval is \lambda.