Often used to model the probability of rare events, for 10 points, identify this probability function, which gives the expected probability of that event occurring within a certain time period and is named for a French mathematician.
Dobinski's formula implies that its nth moment is given by the partitions of a set of size n when it has an expected value of 1. The difference between two of these with different variables and parameters is given by a function named for J.G. Skellam. This function's mean and variance are the parameter itself, which is the product of the number of events times the expectation value, and is represented by lambda. Often used to model the probability of rare events, for 10 points, identify this probability function, which gives the expected probability of that event occurring within a certain time period and is named for a French mathematician.
Dobinski's formula implies that its nth moment is given by the partitions of a set of size n when it has an expected value of 1.
Poisson Distribution