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Hi, I have the following what looks to be simple question:



Suppose N~Poisson(m*theta)

Let X=N/m

Find Pr(X=x) (actually, f(x) is what they ask for, as X won't be discrete)



So I start with

Pr(X<=x)=Pr(N/m<=x)=Pr(N<=xm)



But where do I go from here?

The answer the book gives is: f(x)=Pr(N=xm)



How do I get there? If we employ methods used in continuous distributions, then what happened to the multiplicative factor m when we differentiate?



Many thanks

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