Hello everyone, I've came across this problem and I need to see if my approach is right...
An urn initially contains one Black and one White ball. At each stage, a ball is randomly chosen and then replaced along with another of the same color. Let denote the selection number of the 1st Black ball chosen.
(a)Find the pdf of .
(b)Show that the doesn't exist for .
for (a), I thought that if I came accross a black ball I'll replace it so
and for any .
As for (b), which is 2!!
How could this be?!
Any help is very much appreciated!
No it is not, you are adding white balls to the urn until you get a black ball, so the probabilities change for every draw. For the N-th draw to be the first B requires that the previous N-1 were all W.
it is only valid for N>1, what I wrote was the solution for the recurrence implied in the problem with initial condition p(1)=1/2 (or rather the initial state being (1,1)).What about the 1st selection, we would have a pole!!
If the first draw is W the urn contains 2W and 1B for the second draw so the probability of B on the second draw given that the first was W is 1/3. So the probability that the first B occurs on the 2-nd draw is (1/2)(1/3)
CB
I would like to start by thanking you (oh I will press the "thanks" button), BUT!...
This is my post:
This is how you interpreted the problem:
I don't get how you translated what I said (which was completely vague) into something interesting... Thanks though and you can consider it a closed thread...you are adding white balls to the urn until you get a black ball, so the probabilities change for every draw. For the N-th draw to be the first B requires that the previous N-1 were all W.