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Topic: STATISTICS: Poisson distribution/conditional probablility
Replies: 2   Last Post: Apr 11, 2014 4:37 PM

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 Kathleen Posts: 58 Registered: 12/6/04
STATISTICS: Poisson distribution/conditional probablility
Posted: Jul 22, 1999 10:03 PM

Hello,

I'm stuck again... the question I'm trying to figure out is:

Let X be Poisson(2) be independent of Y which is Poisson(3) and let
W=X+Y. Find the distribution of X conditional on W=10.

Now I have figured out that the sum of two independent random
variables, which have Poisson distribution, also has a Poisson
distribution, specifically of Poisson(a_1+a_2) where a_1, a_2 are the
parameters of the two indep random variables (that was in the qn I did

preceeding this one).

Thus, I know W will have distribution Poisson(5). I also know what
the probablility functions look like for X being Poisson(2) and W
being Poisson(5) are.

Now in order to find the distribution of X conditional on W=10 I want
to figure out P(X|W=10) ... I think this is what I want at least.

Now using the conditional probablility definition you have

P(X|W=10) = P(X,W=10)
----------
P(W=10)

I can easily figure out P(W=10) but my problem is that I don't know
how to figure out P(X,W=10) ... What is this intersection equal to?