# Questions tagged [hypergeometric-distribution]

A discrete distribution used to model sampling without replacement.

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### 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 ...
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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 ...
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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 ...
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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 ...
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### 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 ...
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### 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 ...
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### hypergeometric test for gene feature enrichment on population frequency data

I have a data frame that represents the frequency of gene features in the background population, and several sub populations. For each sub-population, I want to do an enrichment analysis in R with ...
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Is there a profitable strategy for this poker variant? If so, what is the most profitable strategy? Expressed as a percentage of your "special ante", how much would your strategy win on ...
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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 ...
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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 ...
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### 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 ...
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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 ...
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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 ...
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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 ...
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### 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 ...
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### Studies on a special case of the hypergeometric distribution

-Hi, The hypergeomtric distribution is one that is generally intractable to much in depth analysis (i.e. a closed form expression for the median is not known). However, I am working on a problem where ...
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### 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 ...
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### 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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### Comparing a random sample and a non random sample extracted from a finite population

I am not able to formulate a more descriptive title. I have a population of five million people, I code it with R programming language: pop <- 5e6 41% of them ...
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### How to interpret the univariate Fisher's noncentral hypergeometric density PMF?

This is my first time posting so I apologize in advance for any errors! I am struggling to understand the probability mass function (PMF) of the Fisher's noncentral hypergeometric distribution, which ...
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### time complexity of sampling from multivariate hypergeometric distribuiton

numpy has an implementation and the doc is here. It says it is "roughly" equivalent to: ...
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### Connection between Bayesian A/B testing and Fisher's exact test (specific example on Hydroxychloroquine trials)

I understand that there are multiple comparisons floating around between Fisher's Exact Test and Bayesian A/B Testing, here's an example. While I do understand these are fundamentally making different ...
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### Hypothesis testing for large N small k

I've got a set of differentially expressed biomarkers that I want to check for the significance of this observation. For a similar problem, I've seen the hypergeometric test being used, where $k$ = ...
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### How to calculate this dependent probability (marbles without replacement)?

I present the question in two steps: First: Let there be 100 bags. A person puts 5 marbles into 5 separate, randomly selected, bags. You are now to collect the contents of the bags, one by one. If you ...
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### Expected value for a sequence of group samplings from a fixed population

Suppose I've 100 apples where 25 of them are bad and the remaining 75 are good. I draw apples 20-by-20 from this group of apples. That is, I draw the first set of 20 apples from 100 apples, second ...
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### How to compute confidence interval in a case with small sample size, small population size, and one very dominant class?

I have a situation that is analogous to someone starting with a bag of 150 red and blue marbles, and, sampling randomly without replacement, drawing 37 red marbles and 3 blue marbles. What is a ...
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### How can I calculate the continuous cumulitive density function for a hypergeometric distribution?

I have a sample from a large population where it is possible to select either a 1 or a 5. I want to find the probability that the average in any sample is greater than 4.76, and I want to chart the ...
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### Devising an acceptance sampling plan for False Negative Rate

I need to evaluate a binary classifier that classifies inputs in positives and negatives. Since all predicted positives (PP) are assessed, I have complete data on the true positives (TP) and the false ...
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### Quantile (Inverse Cumulative Density) Function for Hypergeometric Distribution

The hypergeometric distribution arises from sampling without replacement. The similar binomial sampling distribution assumes replacement. Hypergeometric distributions are commonly used in quality ...
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### Variance of a hypergeometric distribution

I'm trying to answer the following question from Ross's book: A pond contains 100 fish, of which 30 are carp. If 20 fish are caught, what are the mean and variance of the number of carp among the 20? ...
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### Question regarding MLE

I have a question regarding maximum likelihood estimators/functions. I thought I understood the concept. But now i found an example of an Maximum likelihood function that i don’t get. The question is ...
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### Hypergeometric Probability with a twist

A manufacture receives a lot of 200 parts from vendor. The lot will be unacceptable : If more than five (>5) parts are defective. The manufacturer will select randomly K parts from the lot ...