urn model
- From: isabellesup@xxxxxxxxxxx
- Date: Mon, 9 Jun 2008 07:46:29 -0700 (PDT)
Hi everybody,
I am having a hard time writing the likelihood of the following urn
model. I would need to find the maximum likelihood estimator of p, so
I only need those terms of the likelihood that are functions of p. I
have not seen very many urn problems in my textbooks, if there is a
reference with urn problems, I will gladly read it.
We continue to draw balls with replacement from an urn containing both
black and white balls until two balls of the same color are drawn. Let
X be the number of draws (including the first draw) we take until we
stop. We are not told how many black and white balls that we see, but
only the value of X. Let p be the unknown proportion of white balls in
the urn.
I greatly appreciate your help.
Here is my work so far.
X can take only two values: 2 or 3.
The sample space is
BB, X=2
WW, X=2
BWB, X=3
BWW, X=3
WBB, X=3
WBW, X=3
When X=2, the likelihood can be proportional to p^2 or (1-p)^2.
When X=3, the likelihood can be proportional to p^1*(1-p)^2 or p^2*(1-
p)^1.
.
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