# Questions tagged [hypergeometric]

A discrete distribution used to model sampling without replacement.

139 questions
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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 ...
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### Central Limit Theorem and hypergeometric distribution

We have a game V, which is about pulling 3 cards repeatedly from a deck of 52 cards. For each card with a picture (12 of 52 cards are with a picture) then we win 100 USD of money for each card. We ...
1answer
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### What is the probability that two samples from a source have no overlap?

I picked 29 results from a list of 429 results. I then picked a second group of 27 (with replacement) results from the same list of 429. There was no overlap between the two samples. What is the ...
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### SOA Conditional probability question [closed]

I can't get this correct. Could you please provide a hint to aproach this problem? How do i get the probability of that loss? "A state is starting a lottery game. To enter this lottery, a player ...
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### Probability distribution for draws with conditional replacement? (or how many matches does it take to beat Yugi The Destiny?)

While trying to figure out an old video game, I seem to have stumbled upon a problem that's halfway between a binomial distribution problem and a hyper-geometric distribution problem. With the hopes ...
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### What is the repetition distribution of Pulling balls out of a bag?

I have m balls in a bag, n of them are blue. The target is to pull out k blue balls. (m>n>k) Once I pull out a ball I don't put it back. I want find out the distribution of the number of times I need ...
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### Hypergeometric test for enrichment analysis?

I am referring to a previously asked question on my case for gene enrichment analysis using hypergeometric distribution. Here is my modified question (many thanks to @Glen_b): I have a mixture of ...
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### Modify hypergeometric test?

I have a problem with the fundamentals of hypergeometric distribution for gene enrichment analysis. Here is the problem: I have a set of genes (population size 1500), a mixture of various genes ...
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### Use Fisher's Exact Test or a Hypergeometric Test?

I'm looking to test for set enrichment and I'm wondering whether a fisher's exact test or hypergeometric test is more appropriate (and, if there isn't a straightforward answer, what the relative ...
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### Fisher's exact test for multidimensional contingency tables

I have a dataset that has 6000 instances, each with 8 boolean values. ...
1answer
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### What can I infer from “no evidence” in a hypergeometric distribution sample

I have a population of 320 marbles--they are all supposed to be white, but I can't be certain. If I set a "resolution threshold"--say 5%, then I am hypothesizing there may be up to 16 black marbles. ...
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### min and max of hypergeometric random variable X

I am a bit confused by the min and max values of hypergeometric random variable. Suppose that we have a bag with b blue marbles and r red marbles. we choose k marbles at random (without replacement) ...
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### Hypergeometric distribution when K is unknown

The probability to have $k$ white balls in a sample of size $n$ taken from an urn of $N$ balls with $K$ of them being white is equal to:  P(k|n,N,K) = \frac{{{n}\choose{k}}{{N-n}\choose{K-k}}}{{{N}\...
1answer
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### Chance that sample contains more individuals from one group than from another

Question: 18 men and 12 women have agreed to participate in a randomized controlled experiment. A simple random sample of 15 of these 30 people is chosen as the treatment group; the others ...
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### Hypergeometric distribution and Fisher's exact test

I have looked around but I cannot seem to find a conclusive answer. Does the Hypergeometric distribution assume that the probability of selecting a defective item at any point is equal to that of ...
1answer
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### Multivariate distribution from drawing balls with elimination of previously picked colors from urn at each step

Consider an urn with n balls of k colors ( labelled 1 through k ) where n >= k. You get to draw j times (j <= k) with the following action between draws. Each time you draw a ball belonging to a ...
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### Tests for independence in ragged arrays / bipartite matchings

Let $(Y_i, K_i)$, $i=1,\dotsc,N$ be pairs of observations drawn from discrete labels $L$ and discrete clusters IDs $C$. For example $Y$ could be individual birds, $L$ could be a set of species and \$...
1answer
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### Analyzing a chemistry experiment - Sampling without replacement

I've been reviewing the results of an interesting chemistry experiment a colleague of mine was conducting, and she sought some help analyzing the results. Would you be able to help, please? The ...