# 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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### 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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### Geometric standard deviation on a shifted mean

I want to compute upper and lower control limits for a benchmark value, based on a data series, using geometric mean and a multiple of geometric standard deviation, but am not confident about the ...
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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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### A Multinomial Geometric distribution? What is this distribution called?

In a problem I am dealing with I repeatedly interact with a distribution of the following form, $$p(n_1, n_2, \ldots n_M)=\binom{\sum_{i=1}^Mn_i}{n_1\cdots n_m} w_0\prod_{i=1}^Mw_i^{n_i}$$ where $p$ ...
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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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### 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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### Variance for events occurring with gamma and geometric distribution

I am presented with a problem as follows: A listener is receiving messages with a wait time in between two consecutive messages that is exponentially distributed with a mean of 1 time unit. After any ...
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### Proving that $\lfloor X \rfloor /n$ is a random variable and identifying its distribution. From Probability B. Fristedt

Let $X$ have the exponential distribution. For $n=1,2,\ldots$ let $Y_{n}$ equal $\lfloor X\rfloor /n$. Prove that $Y_{n}$ is a random variable, and calculate and identify its distribution function. ...
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### Geometric distribution with a capped number of trials - finding expectation and prior predictive distribution

So I am modeling a random variable which follows a geometric distribution with probability $\theta$ except that the total number of trials is capped at some value $n$. I.e., the probability mass ...
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### Interpretation of cdf of geometric distribution

Given a geometric random variable $X$ with $p = 0.05$, I want to find (for example) $P(X \gt 10)$. Trivially, this is $1 - P(X\leq10)$, which can be evaluated with the cdf as $1-0.4013$ or $0.5987$. ...
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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 ...
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### Sum of a random number of r.v.'s [closed]

A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, ...
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### Geometric distribution with multiple success state and markovian succes probability

Let $X_t$ be a random process in the space $E:=\{F, S_1, S_2, S_3\}$ for each $t$. We can see it like it is a game where we can win in three different ways or we can fail. We play until we fail for ...
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### Outliers on discrete data

Is there any robust methodology to identify outliers in the discrete data distribution. I am specifically concerned with discrete geometrical distribution? P.S. Data transformation does not seem to ...
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### Difference between geometric distribution and negative binomial distribution

How do I differentiate between a problem of geometric distribution and that of Negative Binomial Distribution? Both include something around first success or failure. I'm confused.
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### Probabilistic user behavior markov models on web

I am considering the following probabilistic Markov model of actions of a user on the results page of a search engine. The user examines the first result, with a probability $A$ he is satisfied with ...
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### Bayesian posterior for Geometric Distribution

I have the following homework problem I am trying to solve for but am stuck with the posterior part. Note the the geometric distribution is a discrete distribution that has a probability mass function ...
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### Unbiased estimator of p in geometric distribution

The answer to this question given by my professor was statistic T(x)= 1when X=0 and T(x) = 0 otherwise. Can I consider E(x) = (1-p)/p and then cross multiply and take 1/(1+x) as an unbiased estimator ...
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### How would I calculate a combination of the Binomial and Geometric Distributions?

To be specific with my problem, I'm calculating a formula for a game. There's 6 independent trials, each with an independent probability of success = 0.34. I know that from the Geometric distribution, ...
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### Distances between random points in a hypercube and statistics of exponents

TL;DR: Why is $\text{avg}\left(|a-b|^k\right)=\frac{2}{(k+1)(k+2)}$? I.e. for $k=2$, as for finding average Euclidian distances, the result is $\frac{1}{6}$? I've been reading a book about "Corobs," ...
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### Geometric distribution with random, varying success probability

I'm really sorry if this question is too basic, but I've been looking for a while and haven't been able to find a convincing response. My statistics background is rather poor. Geometric distribution ...
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### Geometric Distribution - Biased Coin Flip

Whilst studying I stumbled on this problem, which I wish to check if my understanding is correct. Imagine we have a biased coin with probability 'k' of getting a head when flipped. Now A defines the ...
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### Maximum likelihood estimate for geometric distribution from table

I am asked to compute the MLE of the parameter p of the geometric distribution and then apply it to some given data. It is easy to find the MLE: But how do I apply it to these data: ...
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### Geometric Distribution

I'm trying to solve the following problem: The number of bombs required to achieve the disintegration is assumed to be geometrically distributed. In one series in which y bombs are available, x of ...
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### How random variable $Y$ following geometric distribution in the following situation

I have a random variable, $X$ which follows exponential distribution with parameter $\lambda$. Then, define $Y=k$ for some $a$ greater than zero such that: $ka \leq X \leq (k+1)a$. Now, my ...
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### Negative Multinomial Distribution as a sum of random variables

Given a random variable $x$ distributed according to a Negative Binomial distribution with dispersion parameter $r$, it can be seen as the sum of $r$ Geometric distributions. But given the Negative ...
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### What is the probability that a best of seven series goes to the seventh game with negative binomial

Why cant we use negative binomial to calculate the probability of getting a 7th game in best of 7 game series? P(X=7, r=4) = {7-1 C 4 -1} * (.5)^(7-4) * (.5)^4 = .15 , so there is 15 % chance of 7 ...
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### Confidence interval using Central Limit Theorem

I've been trying to find this information online, but have not had much success so far. I want to approximate the 95% confidence interval for the geometric distribution with the following parameters: ...
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### Constant Curve for Cumulative Binomial

I am simulating traffic flow and have come across a rather interesting statistics problem that I'm having trouble wrapping my head around. I am modeling a stretch of road comprised of 2 lanes. Lets ...
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### The special case of the negative binomial, the geometric and calculation with scipy

A particular case? One might consider the geometric distribution is simply a special case of the negative binomial with $N=1$. We know the geometric provides: "The probability the first occurrence ...
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### Proof that the floor of an exponential random variable is a geometric variable

For any real number $x$,$[x]$ represents the smallest integer greater than or equal to $x$. If $X$ is an exponential random variable with mean $1/K$,show that $[X]$ is a geometric random variable with ...
### CRLB for estimating $\theta$ of $\sim\text{Geo}(\theta)$
I'd like to ask if the below computation of the information number for the CRLB is correct: Consider $x_1, x_2$ as iid $\sim Geo(\theta)$ Since $x_1, x_2$ ae iid and the geometric distribution is ...
Let $X \thicksim Negbin(r,p)$ where $(0\lt p \lt 1)$ I want to derive skewness and kurtosis of $X$ by getting the Cgf of X. First, since Followance of Negative Binomial equals to the distribution ...