# 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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### Existence of moment generating function [closed]

Give a example of discrete random variable for which mgf $M(t)=E\left(e^{tx} \right)$ does not exist . I have tried with geometric(p) distribution when $(1−p)e^t≥1$ , the mgf does not converge. Is it ...
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### Likelihood estimation with 2 samples from a geometric distribution

Context Given there are 2 groups that can be modelled as a geometric distribution as follows: \begin{align*} f(x_i;p_1) &= p_1(1-p_1)^{x_i - 1} \; x_i = 1,2,... \; 0<p_1 <1 \\ f(y_i;p_2) &...
1 vote
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### Probability mass function of time of first head

This is an exercise from the probability book by Ross. This is not homework. Using conditional probability and the distribution of sum of two geometric random variables, the probability comes out 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 ...
1 vote
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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 ...
1 vote
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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 ...
861 views

### 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 ...
1 vote
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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.
1 vote
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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 ...