Poisson Distribution
Definition
Definition
Poisson Distribution is used to model the probability distribution for events that happen rarely but at a known expected rate.
Poisson Distribution is used to model the probability distribution for events that happen rarely but at a known expected rate.
P(k, λ) gives the probability for a number of independent occurrences, k, within a given interval for a known constant mean rate, λ.
P(k, λ) gives the probability for a number of independent occurrences, k, within a given interval for a known constant mean rate, λ.
For example, if we know that on average, 2.3 students (per thousand) will fail the statistics course each year. P(3, 2.3) will give the probability of 3 students failing the statistics course in a given year.
For example, if we know that on average, 2.3 students (per thousand) will fail the statistics course each year. P(3, 2.3) will give the probability of 3 students failing the statistics course in a given year.
Explore!
Explore!
Use the applet below to examine how the PDF for the Poisson Distribution changes as the mean changes.
Use the applet below to examine how the PDF for the Poisson Distribution changes as the mean changes.
Red Line = Mean
Red Line = Mean
Challenge 1: Show that sum of P(k, λ) from 0 to infinity gives 1.
Challenge 1: Show that sum of P(k, λ) from 0 to infinity gives 1.
For the Poisson distribution function to be "legit", the sum of all probabilities must give 1, how can this be shown?
For the Poisson distribution function to be "legit", the sum of all probabilities must give 1, how can this be shown?