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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how to get the probability $p=1−(1−1/N)^{Tma_i}$ of extracting at least one ball in the urn

I am reading supplementary information of the paper Activity driven modeling of dynamic networks. It analogys the number of out degree of a activity node by Polya urns problem: it will equal to ...
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Friedman's urn is a supermartingale or a submartingale?

Here is the urn model: At time zero there are $r$ red and $g$ green balls in an urn. At each time-step, we draw out a ball at random and replace it along with $c$ of the same color and $d$ of the ...
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Conditional probabilitiy in balls in urn

A urn has 10 white balls and N black balls. We draw balls without replacement. Given that the second ball drawn from the urn is black, how many black balls must be in the urn such that there is a ...
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Does one-to-one correspondence of the set of sample paths of $X$ and $Y$ imply that $X$ and $Y$ are indistinguishable?

I have two discrete stochastic processes (urn models) $X(t)$ and $Y(t)$. There is a function $\varphi(.)$ such that whenever $\{x_0,x_1,...\}$ is a sample path of $X$ then ...
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multivariate hyper geometric Vs. Indep. drawing without replacement

I think my problem can be seen as a basic urn setup, with another layer tacked on after the fact. I'm looking at drawing from an urn with 3 biological specimens. Each has genotype AA, Aa, or aa. ...
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Polya urn probabilities [closed]

Consider an urn containing two type of balls (red and blue), initially there are $r_0$ red balls and $b_0$ blue balls. At each stage $n\geq 0$ we choose at random one ball, if the ball is red we put ...
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Probability of every ball occurring in multiple independent random samples

An urn contains 5 distinct numbered balls. You choose 2 without replacement. You then reset the urn and choose another 2 without replacement. Do this one more time. Now you have three random samples ...
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What is the distribution of the limit of random variables in a problem involving Polya's Urn?

I know this has been asked elsewhere, but I think the values or random variables are different or something. From Williams' Probability with Martingales: I proved that $M_n$ is a $\sigma(B_1, ...
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References for a Variant of Polya's Urn Scheme

A row of $n_1$ balls, all coloured with colour #1, is laid out before me. I do a set of $k$ replacements (where $k<n_1$) in steps: Step 1: Choose a (uniform) random number $n_2$ on the range ...
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Polya's Urn : proportion Probability

There are two urns with one ball each. Each of subsequent n-2 balls is placed into one of these urns, with probability proportional to the number of balls already in that urn. What is the expected ...
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Expectation of longst run of balls in a Polya-like urn?

We have an urn with $N$ black balls. A single ball is drawn. If the ball is black, it is replaced with a white ball. If the ball is white, it is not replaced. We repeat draws until the urn is ...
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Consecutive Draws from Urn

An urn contains 4 black balls and 6 white balls. What is the probability of getting 1 black ball and 1 white ball in two consecutive draws from the urn? I know this is supposed to be easy. So i tried ...
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Discrete time Pure-Birth process with population fraction

I would like to solve difference equations for a pure-birth process, where the rate of adding new nodes depends on the fraction of population. $$x_i(t+1)-x_i(t)=\alpha ...
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Urn problem: with and without replacement the probability of seeing last ball of particular color

suppose you have red and blue balls in a jar and you pick one at a time, if its red you replace it, additionally you do another draw and throw whichever ball comes up. if its blue you throw it ...
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Counting Operations in the context of an Urn Problem

I was tasked with the following question, regarding the counting of operations in the pseudo code provided that has nested for loops: Let U ={B1,B2,...,Bn} with n >= 3. Interpret the following ...
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Resampling Probability

I've had a student working on some resampling problems. Here's a question I've posed to her: M consecutive draws of size K are taken from an urn with N balls. Balls are replaced between draws. ...
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Formula for urn model with replacement and “color switching”

I tried to figure out following problem, but failed :/ My best guess is that it somehow is a mixture of a binomial and a hypergeometric distribution: I have an urn with N white balls and 0 black ...
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Expected number of red balls removed from an urn before the first black ball

Question: An urn contains n+m balls of which n are red and m are black. They are withdrawn from the urn one at a time and without replacement. Let $X$ be the number of red balls removed before the ...
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Polya's urn model - limit distribution

Let an urn contain w white and b black balls. Draw a ball randomly from the urn and return it together with another ball of the same color. Let $b_n$ be the number of black balls and $w_n$ the number ...
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Multicolored Polya Eggenberger Urn distributions

From an urn containing 1 ball each of $n$ different colours, a ball is drawn, its colour noted and then it is returned to the urn along with $k$ balls of the same colour. what is the limit of the ...
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Number of draws to see every object at least once

I woke up this morning with the following question on my mind: What is (the distribution of) the number of draws you need to sample (with replacement) from an urn with $n$ distinct objects until you ...
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Equilibrium distributions for a finite urn scheme

Given an urn with $n$ (fixed) balls that can be red or black, and given two parameters $0 < p, \, q < 1$, keep doing the following: Flip a $p$-coin. If heads come up, remove a black ball or ...