Simeon Desnis Possion was the person who discovered this distribution. This is also pronounced as "Pwason". This probability distribution expresses the probability of a no. of events occuring in a fixed period of time if these events occurs with a average rate and independently of the time since the last event happened.
This distribution is mainly used for the number of events in a specified intervals such as distance , area or volume.
The fomula given my Possion is as :
f ( k ; y) = y power k x e power -y / K !
where -
e is the base of natural logarthim (e = 2.71828...)
k is the number of occurrences of an event - the probability of which is given by the function
k! is the factorial of k
y is a positive real number , equal to the expected number of occurrences that occur during the given interval. For instance, if the events occur on average 4 times per minute , and you are interested in the number of events occurring in a 10 minute interval, you would use as your model a Poisson distribution with y = 10×4 = 40.
The Poisson distribution can be applied to systems with a large number of possible events, each of which is rare. A classic example is the nuclear decay of atoms or the no. of accidents happened due to the fallen from roof in a metro city.
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