# 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'.

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### Difference between geometric distribution expectation and 1 - failure with Binomial

I'm trying to understand a simple problem: How many times you'd need to roll two dice to get two ones in a single roll. One way I see this is as a problem the geometric distribution describes. You ...
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### Non-informative prior of a geometric distribution [duplicate]

If we are given a standard geometric distribution $(1-p)^{x-1} p$, with $0<p<1$ what would be a suitable non-informative prior for this?
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### What statistical distribution would best capture a set of Wordle outcomes?

Wordle is a simple and popular word game. It is based on an older game, and has recently gone viral and attracted attention. It is available in several languages and the original site (now owned by ...
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### Statistical test for geometric distribution

Question I have a sample of data (~250 values) which I think is geometrically distributed. Is there any statistical test that I can use to check if it is indeed geometrically distributed? Ideally ...
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### Finding the distributions of the max and min of random variables from the geometric distribution

Let $X$ and $Y$ be independent random variables following the same geometric distribution, that is $P(X=k)=P(Y=k) = (1-p)p^k, k=0,1,\ldots,$. Let $U=min\{X,Y\}$, $V=max\{X,Y\}$,and $W=V-U$. How do I ...
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### Geometric Distribution in R

I'm trying to solve a problem involving a Geometric Distribution with $p = 0.20$ and $x = 5$. I use the formula and R, but I get two different answers: \begin{eqnarray*} P(X = x) & = & p(1 - p)...
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### Bias correction for MLE of mean of geometric random variable

Parameter estimation [ edit] For both variants of the geometric distribution, the parameter $p$ can be estimated by equating the expected value with the sample mean. This is the method of moments, ...
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### A description of the mean of the Geometric Distribution - is it unorthodox or just incorrect?

I have a homework assignment where I'm asked to propose an estimator for the mean of a geometric random variable. This seemed simple enough, given that I've always understood the mean of the geometric ...
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### Number of tries until Failure with n different independent Bernoulli experiment

I have 3(n) coffee machines in an office. I have a historical log of these machines, and I know in the last ten days(t) how many times they failed to make a coffee. For example: machine 1: 10 ...
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### KS goodness of fit test result for geometric distribution low p-value [duplicate]

I am trying to test if the sampled interval between random events fits a particular geometric distribution, and am pretty lost as to what I'm doing wrong. Assuming there's nothing wrong with the ...
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### If Distribution is Geometric does that mean underlying probability of success for each trial p is fixed?

we know that if p (probability of success at each trial is fixed then the probability of each trial, then probability of first success at kth trial is given by Geometric Distribution I need to ...
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### Strange connection between Bernouilli, Uniform and Geometric distributions

Final update on 11/29/2019: I have worked on this a bit more, and wrote an article summarizing all the main findings. You can read it here. Let us consider $Z = X_1 + X_1 X_2 + X_1 X_2 X_3 +\cdots$ ...
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### Given a geometric random variable, why is it that $P(X > x) = (1 - \theta)^x$ and not $\theta(1 - \theta)^x$?

Suppose $X$ ~ $Geometric(\theta)$, where the distribution is based on identically independent Bernoulli trials (each trial has $\theta$ = probability of a success). The distribution is for the number ...
I'm attempting an assignment in which we're supposed to write a function to simulate a geometric distribution with $p=0.03$. While plotting a histograms for about $100000$ simulations of the function, ...
### How to work out the expected value of $X^3$ for a geometric distribution
I have scoured all my textbooks and all through the internet but haven't been able to find a suitable answer to this. I have struggled my way through finding the expected value of $X^2$, with the help ...