Probability Distribution and Shape

> restart;

> with(plots):

>

The Poisson Distribution

The Poisson( ) distribution is a discrete distribution on the non-negative integers {0,1,2,...}.

The parameter must be positive.

If X is a random variable having the Poisson( ) distribution, then the probability distribution

function for X is

f ( k ) = P( X = k ) = , k = 0, 1, 2, ...

Recall the convention 0! = 1.

The following code will draw a probability histogram for the Poisson( ) distribution

for =2, but you are encouraged to try other values of .

> lambda:=2;

> ProbHist(PoissonPDF(lambda,x),0..20,21);

To see the effect of on the shape of the Poisson( ) distribution, the following

animation will draw a series of probability histograms as varies from 1 to 15.

> for n from 1 to 15 do

> num:=convert(evalf(n), string):

> tracker[n]:=textplot([18,0.3,`Lambda is `.num],color=blue):

> H[n]:=ProbHist(PoissonPDF(n,x),0..25,26):

> P[n]:=display({H[n],tracker[n]}):

> od:

> display([seq(P[n], n=1..15)], insequence=true,title="Lambda is Increasing from 1 to 15");

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