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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Confused about geometric distribution [duplicate]

So I have a game that follows a geometric distribution. There is a probability, $p$, of winning a round. If the player wins, he earns \$1,000. As soon as there is a win, the game ends. If the player ...
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Geometric Distribution: Playing a Game with Cost

Suppose I have \$3,000. I play a game, for which I have a probability $p$ of winning. I have to pay \$300 each time I play the game. If I win, then I earn a payoff of \$500. I can play the game as ...
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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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Bayesian Discrete Survival Analysis

I've been reading over Bruce Hardie's tutorial on survival analysis of customers in a discrete-time subscription model. Two design choices he delineates early on include the Geometric PMF: $P(T=t|\...
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What is the expectation of $e^X$, where $X$ is a random variable with a geometric distribution?

if $X$ is a random variable how can I calculate $$ E(e^X) $$ I have no idea on how to do that.
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Concentration of sum of geometric random variables taken to a power

I am interested in techniques for showing the concentration of sum of $n$ iid geometric random variables $X_1, X_2, \cdots, X_n$ (number of trials until success), say with success probability $p = 1/2$...
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Accurately estimating the parameters for mixture of geometric distributions

Say we have an i.i.d. sample from a mixture of Geometric distributions: $$ \begin{cases} Geo(p_1) &w.p. \pi_1\\ Geo(p_2) &w.p. 1- \pi_1 \end{cases} $$ Call the parameter set ${\theta}=(\pi_1,...
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Intution about the memoryless property of geometric distribution [duplicate]

I was watching the video about the memoryless property of geometric distribution. Here is an excerpt from the video. $$\begin{aligned} P(X \geq x+y \mid X \geq x) &=\frac{P(X \geq x+y, X \geq x)}...
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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 ...
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Which of two parameters was chosen for a sample?

Problem: $X$ is chosen to be $\text{Geom}(p_1)$ with probability $\frac{1}{2}$ and is otherwise chosen to be $\text{Geom}(p_2)$. Given a sample of size $n$ from $X$, guess whether $p_1$ or $p_2$ was ...
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Equivalence of two state Markov chain and sampling via geometric distribution

Let $\mathcal T = \{1,2,\ldots,T\}$ denote the set of points in time, $S = \{0,1\}$ the state space, $X = (X_t)_{t \in \mathcal T} \in S^\mathcal T$ a time series, $\alpha = \mathbb P(X_{t+1} = 0 \mid ...
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Does density belong to exponential family?

$$f(x;\theta) = 2x\theta\exp({-x^2})\left( \frac{\exp({-x^2})}{1-\exp({-x^2})}\right)^{\theta\ - 1}\mathbb I_{(\mathbb R_{++})}(x) $$ with $\theta \in \mathbb R_{++} $ does $f(x;\theta)$ belong to ...
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Number of trials to observe an inconsistent outcome in Bernoulli distribution

Suppose I have a random variable $X$ following a Bernoulli distribution with some known probability $p$. How do I calculate the mean number of trials $N$ needed such that you'd expect to observe an ...
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How to find the average distance between randomly distributed points in a rectangle?

Assume there are n points randomly distributed in a rectangle (x being the height y being the width) shown below in the figure. I would like to calculate the average distance between 2 random red ...
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Probability exercise using geometric distribution---Roulette gambling

A gambler plays roulette at Monte Carlo and continues gambling, wagering the same amount each time on “Red”, until he wins for the first time. If the probability of “Red” is 18 and the gambler has ...
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Can you write a Geometric random variable as some combination of Bernoulli random variables?

Background Given $Y \sim \text{Binomial(n,p)}$, we can write $Y = \sum_{i=1}^{n} X_i$ where $X_1,X_2,...,X_n$ are iid $\text{Bernoulli}(p)$. This is useful in, for example, determining the mean of a ...
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Which variation estimate to prefer: SD, geomSD, CV?

I have a case where we see regional disparities in median received services. Services is a lognormally distributed variable. Plot is based on a lognormal model, examining y and sigma. You can see that ...
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Test statistic for the geometric distribution

I start with a sampling distribution of an unknown discrete probability distribution with PMF $g(x)$. I want to test if this distribution is in fact a geometric distribution, this is my $H_0$. ...
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can you look this problem and solution?

A company produces IC (integrated-circuit) chips. (a) The produced chips are tested one at a time until a good chip is found. If the probability that at least three tests are needed equals 0.0225. ...
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can you guide me how can ı solve this?

Missiles are launched until one successfully reaches the target. If the expected number of launches is 2.5, find the probability that at most 3 attempts will be needed.
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Intuition behind memoryless process and geometric series

I was reading this problem (Page 6, THE BASKETBALL PROBLEM, MEMORYLESS PROCESSES AND THE GEOMETRIC SERIES) and stumbled upon the solution using the memoryless property. I cannot understand the ...
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Sample log geometric distribution from log probability

I want to sample from the geometric distribution for a very small success rate. The success rate is so small that I represent it by its log. I want the result to also be represented by its log. Is ...
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What does $E(X = k)$ mean if $X \sim Geom(p)$?

So, I have the following question for homework assignment: $X_{1}$, $X_{2}$ have geometric distributions with parameters $p$ and $1-p$ respectively, $X_{1} \sim Geom(p)$, $X_{2} \sim Geom(1-p)$. $X_{1}...
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Estimating the blockchain mining time for $N$ nodes

I am trying to simulate a set of times for the below problem. There are N nodes. Each node generates a random number($R$) in the range $[0,K]$ per second. Guess the time it takes by each node to ...
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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 ...
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Based on the record X1 ,…, Xn what is the unbiased estimation of 1/p [duplicate]

If we investigate $n$ patients for SARS. The indicator of sequence of the trails is $X_i$ ($X_i=1$ is for success and $0$ is not success). And the sequence indicator is available for all n independent ...
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Flat "geometric distribution" by varying the probability of the Bernoulli trail

In a simulation I am working on, each day (time step) there is a chance that a condition changes (at which point it is stuck in the changed condition). Setting this probability to a fixed value (say 5%...
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Inferring an approximate distribution for noising of data given 300,000 samples of human noising [closed]

I'm trying to find a statistical way to get an approximate distribution of all human noising. I have a dataset of over 300,000 samples of people noising words. I took basic Statistics and I would know ...
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Geometric distribution: finding canonical link and proving it is part of the natural exponential family?

Looking for some help on my statistics homework question! The background to the question is: suppose that you toss a biased coin repeatedly (and independently) until you get a head. Let Y denote the ...
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Proper length of random nonce for hash calculation (blockchain)?

I have a string s and I need to calculate a nonce such that when appending the nonce to the string, the generated hash starts with a given sequence. The hash has 256 bits, so the number of ...
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3 votes
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What is the expected waiting time to have at least k members, knowing that each member is drawn from a population size N with the probability of p?

Consider a population of size N. Each day, each member of the population is drawn without replacement with the probability of p ...
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R - Geometric Distribition

Why pgeom(20,0.01,lower.tail = FALSE) 1-sum(dgeom(1:20,0.01)) produce different results in R? The result should be the same (...
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Expected number of tosses until winner in game with two players with two different coins

Two players each have a coin which gives heads with probability $0.7$ (player 1) and $0.3$ (player 2), respectively. Player 1 goes first, and the players alternate until someone gets heads. What ...
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ANOVA-like analysis for geometric distribution

I have a dataset (>10,000 samples total) that strongly appears to be geometrically distributed. For this dataset I have a way of partitioning that makes sense theoretically and I would like to know if ...
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Does the 10% condition apply to geometric distributions?

I know that the 10% condition is required to assume independence in binomial settings. However, in a geometric setting where there is no fixed n-value, how would one determine independence? I am a ...
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When (if ever) is the sum of two dependent geometric RVs negative binominal?

Imagine you have two random variables $X $ and $Y$, you know $$ X \sim \text{Geometric}(p) \\ X + Y \sim \text{Negative Binomial}(2, p) $$ I am interested in what if anything can be said about 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 ...
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2 votes
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Gaps in histogram for geometric distribution

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, ...
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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 ...
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