Questions tagged [polya-urn-model]

In the basic Pólya urn model, the urn contains x white and y black balls; one ball is drawn randomly from the urn and its color observed; it is then replaced in the urn, and an additional ball of the same color is added to the urn.

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Question on the expected number of same color balls left in a urn

I'm working on a problem where I am given an urn with $a$ white balls and $b$ black balls. One ball at a time is selected randomly until there is only balls of the same color. I am asked to find the ...
• 125
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Polya urn scheme by induction task

I've been trying to solve the task given in "An Introduction to Probability Theory and Its Applications" by William Feller. The task is to show by induction that the probability of a black ...
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Asymptotic behaviour of the difference process of the Polya urn

Assume we have a Polya urn with $(a,b)$ initial (time t=0) red and green balls, respectively. At each point in time we draw a ball at random and add it back together with further $S$ balls. This means ...
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We draw a ball, look at it, then return it to the urn and add another ball of the same color. Pr: "after $n$ draws the urn contains $j$ white balls"?

The urn contains $1$ white ball and $1$ black ball. We make a sequence of $n$ draws according to the following scheme: we draw a ball, look at it, then return it to the urn and add another ball of the ...
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How to get this formula for expectation of continuous-time urn process

We define the continuous-time, multi-type branching process $(X(t))_{t\ge0}$ as follows: $(X(0))=\alpha\in\mathbb{R}^d$, where $\alpha=(\alpha_1,\dots,\alpha_d)$ is the urn initial composition, ...
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