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Questions tagged [geometric-distribution]

The geometric distribution is a discrete (count) distribution, where the probability of each count is a constant proportion of the next lower count. An example is 'the number of coin tosses until the first head'.

The geometric distribution is a discrete distribution. The probability of each value after the first is a constant proportion of the next lower value.

The geometric distribution is a special case of the negative binomial. It is the probability of a particular kind of count in a set of Bernoulli trials - and may be defined either as the number of trials or the number of failures to the first success (the count thereby being at least 1 or at least 0 respectively). An example is 'the number of coin tosses until the first head'.

See also: https://en.wikipedia.org/wiki/Geometric_distribution

References:
Wikipedia: Geometric distribution
Mathworld: Geometric Distribution

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Comparison of waiting times to geometric distribution

I am analysing data taken from observing about one million people over 24 months. For each person, each month is classified as a "success" or a "failure". I am specifically interested in the distribution of waiting times (= the lengths of runs of…
Dzamo Norton
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First Success distribution with geometrically decreasing success probability?

If a treatment has constant success probability of $p$ per trial, the probability of success on trial $k$ is given by the First Success Distribution. $$P(K\!=\!k\,|\,p) = p(1-p)^{k-1} \qquad k = 1, 2, 3, ...$$ Let $q = 1-p$, $$P(K\!=\! k\,|\,p) =…
Mkanders
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Is this a geometric distribution problem?

Suppose a student starts with test A, and will proceed to test B, then test C if he passes. The probability for the student to pass test A is 30%. The probability for the student to pass test B is 20%. The probability for the student to pass test C…
user7381027
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Given a success on the kth trial, the probability of success on the mth trial

I know that this form of the Geometric distribution gives the probability that for a success probability $p$, the kth trial out of k trials is the first success. $Pr(X=k) = (1-p)^{k-1}p$ My question is, conditioned on the first success happening on…
TSP
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Geometric distribution with multiple trials

I was looking into geometric distributions to find the probability of the first success of some random variable X. So if p = 0.04, the geometric distribution looks something like this: I understand the graph mathematically from the probability…
Ken
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Parallel between probability,wait time, frequency and period

I was reading about the geometric distribution, where $E(X) = 1/p$. This made me think of the classic formula in physics: $t=1/f$. Is there a parallel between both formulas, especially since a probability is often viewed as a frequency, and, on the…
Ant
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unbiased estimate of a geometric model

I was reading a book where in one of the section it shows how to find the unbiased estimate of a geometric model. This is from the book: Let x denote $n =1$ realisation from a geometric $Geom(\pi)$ distribution with pmf $f(x;\pi) =…
john_w
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Is it possible to view sequential independent trials as pre-determined with unknown outcome?

This question is best represented by the following short story: Alice and Bob have been captured and imprisoned on an island by an evil adversary. Each day they are captured there the jailer rolls a fair 100 sided dice and announces the result,…
Jack Arthur
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