Suppose X = A*N, where A is a scalar constant and N ~ Pois(lambda).
Then P[X = x] = P[N = x/A] ~ Pois(lambda).
I.e., X has the same probability mass distribution as N, except for a
scale factor of A on the assumed values.
I think you are thinking this problem is complex, when, in fact, it is trivial.
At 07:41 AM 5/12/2009, Jewel Bright wrote:
Folks:
I have a seemingly simple question, but cannot resolve it (at least
without much of thinking and digging.
Suppose that "n" is a Poisson random variable drawn from the
distribution with Poisson lambda "lambda". What is the distribution
of the random variable A*n, where A is an arbitrary real number?
Please, note, I am not asking how to generate this random variable,
I still remember how to multiply a set of numbers by a constant. I
am asking about analytical form of this distribution, and about how
to derive the distribution function (or density) in their analytical form.
A standard approach through the characteristic functions did not
bring immediate success. I am sure there there are a lot of smart
people in the list who would consider this problem very simple. Please, help.
Thanks in advance.
Jewel
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