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Tech Tips: Poisson Distributions

Calculating P(X=x) when X follows a Poisson Distribution

Suppose one wishes to find the Poisson probability of seeing exactly k occurrences of some event within some well-defined interval, where the mean number of occurrences in that interval is expected to be λ. That is to say, we seek

P(k)=eλλkk!

To do this one should ...


Calculating Cumulative Probabilities when X follows a Poisson Distribution

Suppose one wishes to fine the cumulative Poisson probability of seeing k or fewer occurrences of some event within some well-defined interval or range, where the mean number of occurrences in that interval is expected to be λ. That is to say, we seek P(Xk)=P(0)+P(1)+P(2)++P(k)=0ikeλλkk! To do this, one should ...


Simulating Random Variables following Poisson Distributions

To generate n realizations of a random variable that follows a Poisson distribution, counting the number of occurrences of some event within some well-defined interval or range, where the mean number of occurrences in that interval is expected to be λ. ...