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Questions tagged [hypergeometric-distribution]

A discrete distribution used to model sampling without replacement.

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Estimating the Likelihood of Finding New Accessibility Issues in Mobile Applications

I have an algorithm designed to identify accessibility issues in mobile applications. The algorithm itself has some bugs (issues), and I aim to project the likelihood of discovering a new issue with ...
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Confidence intervals when using stratified proportionate random sampling

I have hypergeometric distribution with population size N. I need to estimate population proportion p. I would like to use confidence interval. I have also three non-overlapped groups in my population....
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Mark recapture with no knowledge of marked individuals

I am a math student working with a group of field biologists. In multiple experiments of mark-recapture of the same population, they claimed that if the number of observations (recaptures) is large ...
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Fitting Hypergeometric distribution requires non-integer arguments?

I have a vector (length s) of observations, x are class "0" and s-x are class "1" and are drawn from a population of size N. Hence, they follow the hypergeometric distribution: $$H(...
Jesús Castrejón's user avatar
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Probability of selecting 4 cards that add up to 5 from a deck of 40 cards

Let's say we have a deck of cards excluding face cards, so cards from Ace to 10. Which of these is the correct way of computing the probability that the sum of 4 randomly chosen cards is equal to 5? ...
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Is there an additive property for hypergeometric random variables?

I know that for binomial and negative binomial RVs there is an additive property where if $X_1\sim bin(a, p)$ and $X_2\sim bin(b, p)$ then $X_1+X2 \sim bin(a+b, p)$ if $Y_1\sim NB(c, p)$ and $Y_1\sim ...
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Analyzing Cumulative Distribution Functions in Sampling Without Replacement vs. With Replacement

Originally asked on MATHEMATICS. I am studying a population of $N$ bits, comprising $K$ ones and $N-K$ zeros. For sampling $n$ bits without replacement, the situation conforms to a hypergeometric ...
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Analogue of fisher's exact test for one group?

I understand that Fisher's exact test applies to testing whether the proportion of an outcome in one group, $p_1$, differs from the proportion of the outcome in another group, $p_2$. This could be ...
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Concentration inequality for hypergeometric distribution

Let a population $C$ consist of $N$ values $c_1, c_2, \cdots, c_N$, with $c_i\in \{0,1\}$. Let $X_1, X_2, \cdots, X_n$ denote a random sample without replacement from $C$ and let $Y_1, Y_2, \cdots, ...
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drawing from multiple urns based on a random number

Suppose I have $N$ numbered urns, each with different colored balls. Now I have some fixed discrete distribution that I use to draw a random number $i \in \{1 ... N\}$. I now pick a ball from urn $i$, ...
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Estimating parameters of hypergeometric distribution when population size is unknown

I am given a bag containing marbles of two colors, with an unknown total number of marbles $N$. I randomly sample $n$ marbles ($n=n_1+n_2 < N$, where $n_1$ and $n_2$ are the number or marbles of ...
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Conditional probability given conditional probabilities [closed]

If $X$ and $Y$ are independent binomial random variables with identical parameters $n$ and $p$, show analytically that the conditional probability of $X$, given that $X + Y = m$ is the hypergeometric ...
Elizabeth Junior Asomaniwaa's user avatar
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Binomial distribution but only failures are replaced

I might be thinking about this in a completely wrong way, but I have the following problem: Let's say we have 100 people in the population, and we know the probability of someone dying on any given ...
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Vapnik-Chervonenkis dimension of hypergraph, given bound on number of hyperedges

in studying now about Vapnik-Chervonenkis dimension, and there is one question that I not able to solve. Let $\textrm{(X , R)}$ be a range space so that any hypergraph $\textrm{(V, F)}$ in it ...
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UMP test for hypergeometric distribution

$P(X=x|N,D,n)=\frac{^DC_x \times ^{(N-D)}C_{(n-x)}}{^NC_n}$ Now, I was trying to test for $H_0:D\le D_0$ vs $H_1:D>D_0$ using likelihood ratio test. But to find the maximum likelihood estimate of $...
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Binomial Proportions when sampling without replacement not studied?

Question When doing surveys with a population, we obviously don't replace by design. Why is it then that the mathematics and statistics described in textbooks seems to be veering more on the side of ...
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1 vote
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Sample Size Determination for Hypergeometric Rare Event

Suppose that there are 10 smokers and 590 non-smokers in a room and let $X$ be a random variable that describes the number of smokers picked out, without replacement, in $n$ random draws. What methods ...
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Best way to check that categorical data have not been shuffled

Someone has done a survey, asking a list of $N$ people if they were married ($M$) or single ($S$). You get the result as a table with two columns, 'Name' (text, all unique values) and 'Status' (...
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Probability of getting k different colored balls from an urn with K different colors of balls, each color has the same number of balls

Let's say I have an urn with $n$ balls, with $K$ different colors of balls, where each color has the same number of balls: $\frac{n}{K}$. Given I reach into the urn and grab a ball (without ...
Quantum Guy 123's user avatar
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What is correct way to calculate the expected overlap of protein sets in two related biological system

I have a question regarding the statistics of protein set differences in two biological samples. I have performed quantitative proteomics analyses on both WT and KO cells (derived from the WT cells by ...
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Does the hypergeometric distribution follow a Bernoulli process?

There is a comment in an online resource that I need help understanding: In a Bernoulli process, given that there are M successes among N trials, the number X of successes among the first n trials ...
Snehal Patel's user avatar
12 votes
3 answers
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How do you calculate the expected value of a discrete distribution without replacement?

Say I have a set of 10 values I want to draw 3 values from, uniformly, without replacement. For instance: $$S = \{0,0,0,0,22.95,0,0,0,19.125,25.5\}$$ With replacement, this seems simple, you just add ...
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how does adding information change the probability of an event?

In a comedy TV programme, four men are sitting at the bar. The barman tells them: "Did you know that, statistically, one out of four men is having an affair?". The first man replies "...
user6376297's user avatar
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Drawing 0 green balls from an Urn with non-uniform probabilities

An urn contains $N_1$ red balls and $N_2$ green balls. Each ball has an associated weight. Each ball is drawn (without replacement) with a probability proportional to how much its weight contributes ...
Cohensius's user avatar
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How to estimate the parameters of a hypergeomtric distribution?

I am looking for some guidance on how to estimate the parameters of a hyper-geometric distribution, based on a random sample. For example, if I generate a distribution as follows: ...
Jonathan Dunne's user avatar
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What distribution does a ratio of successes to failures (with replacement) follow?

Suppose you realize $n$ draws—with no replacement—from a sample of $N$ marbles, in which I know there are $K$ white marbles and $N - K$ black marbles. The probability of getting $k \leq n$ white ...
Daniel Pérez's user avatar
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Are the reported odds to win Lotto Max on https://playalberta.ca/games/lotto-max incorrect?

The Alberta Lottery displays the odds to win various Lotto Max prizes on their website here . Each $5 wager contains 3 sets of 7 numbers. The winning numbers are drawn from a pool of 50, so the ...
Jared's user avatar
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A variation of the Lady Tea Tasting problem [closed]

I am quite stuck on this question. My intuition would have been to say that we would prefer to pour milk first on heads, but I am not sure. The setting is: the Lady guesses "milk first" in 2/...
Waikiki's user avatar
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Combinatorics - calculating probability of choosing n people from m groups of k people

I am trying to calculate and understand the following question: I have 10 groups of 10 people each and am choosing 10 people at random. What is the probability that all 10 people I have chosen are ...
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Sampling identical sequences from two urns with unique colored balls

In very simple terms, my problem is as follows: given two urns, both with N balls where each ball has a unique color, I am interested in sampling sequences of N balls without replacement from each urn....
Doa's user avatar
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Is There a Conjugate Prior for a Multivariate Hypergeometric Likelihood?

I am working on a problem using a multivariate hypergeometric likelihood. The multivariate hypergeometric distribution does not belong to the exponential family of distributions, so (to my knowledge) ...
Ryan Folks's user avatar
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Game design urn problem

I am designing a tabletop game and trying to conceptualise the probabilities involved. These can be expressed as an urn problem: Our urn contains seven counters, either green or red. We draw five and ...
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Test change in intersection between two sets of subsets

let's say I have a set A, and a set B, both subsets of C. To test whether A and B have statistically greater overlap, I can use the hypergeometric test. However, let's say I now have: $A_1, B_1 \in ...
G D's user avatar
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3 votes
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How many orders will be placed on average until stock runs out, given a probability that the customer will find the item they want?

Let there be 500 units of stock $s$ of diverse items in a store. Customers arrive one by one and, for every given item, there is a likelihood $m$ of 5% that it is precisely the item that the customer ...
Pedro Schuller's user avatar
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2 answers
215 views

Multivariate Hypergeometic Distribution with overlapping events

I have a deck of 52 playing cards and I play a game where I need a combination of specific card categories to make combos. For example: I draw 5 cards as a sample hand and I need exactly 1 Jack and 1 ...
LADD's user avatar
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1 vote
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Hypergeometric distribution with no number of defect items information

So I am looking at the problem here: A hospital has received a shipment of 25 new X-ray machines. The hospital could lose its license for housing X-ray machines if the machines are not properly ...
Paul726's user avatar
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2 votes
1 answer
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What is the best way to test of draws ( 10,000 unique possibilities) from multiple sample are random?

say I have 6 people drawing from their own box, each box contains 10,000 unique barcodes. Now at the end of the experiment each person has drawn roughly 10-20 barcodes. How do I test if the barcodes ...
Ahdee's user avatar
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Intuition for hypergeometric variance?

I'm trying to learn the major facts about a bunch of probability distributions, hypergeometric included. I can use the commonalities between it and a binomial to my advantage for thinking through some ...
Mr. Bultitude's user avatar
4 votes
1 answer
56 views

Percent chance that two samples are different population (NPS)

Practical question (not a statistician), I want to make a PPT slide (amongst several) in a business discussion, related to comparing a new survey with an old one. Want to be able to say something to ...
PPT slide writer's user avatar
1 vote
1 answer
707 views

Draw two balls without replacement

Suppose we consider an urn with 3 red balls and 5 blue balls. We now draw two balls without replacement. If we draw a red, it is a success otherwise a failure. Let X=1 if we draw a red ball in the ...
Kenneth's user avatar
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2 votes
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How to calculate $Var(X)$ for the union size?

Let's say there is a set of $4$ bags $\{{a,b,c,d\}}$ containing balls of colors $\{{red,blue,green,orange,black\}}$. Balls are assigned to bags in an arrangement that allows a variable number of ...
ilibarra's user avatar
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Finite population correction for Binomial distribution without Normal approximation

I would like to evaluate the quantile function for a binomially-distributed random variable $X\sim Bin(n,p)$, where $n\ge 1000$. There are a couple of problems: The number of trials $n$ is very close ...
demim00nde's user avatar
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When is it justified to assume a hypergeometric distributions for power analysis and hypothesis testing

Suppose a car rental company historically only rented white cars, and they want to to test if red cars make customers more likely to pay for an upgrade, such as enabling satellite radio. (I am just ...
Joe's user avatar
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3 votes
1 answer
5k views

Binomial vs hypergeometric finite sampling distribution

I was reading these notes:Finite Population Sampling with Application to the Hypergeometric Distribution and I have a question just about the first two pages. The first page, they derive the variance ...
Steve's user avatar
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1 vote
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Exercise on MLE with hypergeometric distribution

I am struggling with the following exercise from Stapleton's book (it's exercise 7.4.1). A box contains eight eggs, of which an unknown number $R$ are rotten. You take a simple random sample of three ...
J. D.'s user avatar
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0 answers
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Using hypergeometric test for presence/absence of different conditions

My dataset consists of 3 conditions, with different numbers of samples in each condition (30 in condition 1, 80 in condition 2, 50 in condition 3). I have measured the presence or absence of a gene in ...
Elliot's user avatar
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1 vote
1 answer
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Drawing a random sample without replacement from data set

I have data generated by a RCT with a control and treatment group, each with n=300, so N=600. The observations are assumed to be i.i.d.. From that population, I'd like to draw 5 random observations ...
Marc J. Muller's user avatar
4 votes
1 answer
157 views

Is this a Hypergeometric Distribution Problem?

There are $100$ people who bought a ticket for a raffle with $5$ prizes being offered. They randomly draw a name for the $5^{th}$ place prize, then they randomly draw a name for the $4^{th}$ place ...
BonnieKlein's user avatar
3 votes
1 answer
52 views

How to determine odds in a game similar to roulette

A game similar to Roulette has 360 slots. 20 of these slots are 'scoring' positions. Each slot will only accomodate 1 ball. If a number of balls are introduced (Say 3) What are the chances that any 1 ...
Brian Doyle's user avatar
0 votes
3 answers
166 views

Probability of drawing two differently colored balls in a partition of equally sized partitions

If I randomly distribute, say, 100 red and 10 blue balls onto a field of 10000 square meters (100*100 m), how would one calculate the chance of having at least one red and at least on blue in the same ...
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