Questions tagged [hypergeometric-distribution]

A discrete distribution used to model sampling without replacement.

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7 votes
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Geometric distribution without replacement

On an attempt to solve this problem I've managed to reduce it to finding the expected number of white balls picked until one black ball is observed (let's call that value $v$). Except that, unlike the ...
Mohammad Alaggan's user avatar
3 votes
1 answer

Hypergeometric trials - Number of trials needed to achieve a given probability

Given a known number of white and black balls in an urn, what is the number of trials without replacement required to achieve a given x probability of drawing at least one white ball. Which function ...
ECII's user avatar
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11 votes
3 answers

What is the probability of n people from a list of m people being in a random selection of x people from a list of y people?

If I am selecting 232 people from a pool of 363 people without replacement what is the probability of 2 of a list of 12 specific people being in that selection? This is a random draw for an ultra ...
Sarge's user avatar
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0 votes
1 answer

Closed form solution for the expectation of the square root of a hypergeometric variate

As the title states, is there a closed form formula for the expectation of the square root of a hypergeometric variable. Edit: Closed form approximate solutions based on related distributions or ...
hyper's user avatar
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3 votes
0 answers

Distribution of the size of overlap between two random samples with duplicates?

Similar to this question, I want to know if the overlap between two samples is significant. However, my items are not unique; I have $c$ distinct colors of items, there are $m_i$ items of color $i: (...
Jay Hacker's user avatar
5 votes
0 answers

Using the hypergeometric distribution for skipping events in transcriptome sequencing

My question is inspired by this post. However, its a bit more complicated than that to explain. I hope I succeed. I work with RNA-Seq data on alternative splicing in plants. For this discussion, lets ...
Arun's user avatar
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4 votes
1 answer

Sum or mean of several related hypergeometric distributions

I have an odd problem which can be phrased in a general way, and a more specific way. I'm curious about the answers to both. Although, really, it's the k=0 case that I'm really interested in - ...
jebyrnes's user avatar
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4 votes
1 answer

Lower bound for tail of hypergeometric distribution

There are several simple and widely used upper bounds on the tail of the hypergeometric distribution, including $P(X > E[X]+tn) <= e^{-2t^{2}n}$, where X is hypergeometric with parameters N, M, ...
DavidDLewis's user avatar
6 votes
2 answers

Probability of drawing no red balls from 20 draws without replacement given finite sample

I understand this to be a binomial distribution: There are 100 balls in a bucket. 10 are red, 90 are blue. I select a ball at random and then replace it in the bucket, and I do this 20 times. I then ...
Mark Nice's user avatar

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