# 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'.

165 questions
Filter by
Sorted by
Tagged with
20 views

### Nonhomogenous Geometric Distribution Approach

I am trying to solve this problem by considering a geometric distribution with unequal probabilities. First, I am using the Irwin-Hall Distribution to deduce that for n independent uniform random ...
• 21
119 views

### Geometric distribution expected value proof doubts

Hello, I have problems understanding the proof for the expected value of geometric distributions. I don't know why the bound upper is set to infinity. For binomial distributions, the upper bound of ...
22 views

• 41
1 vote
45 views

### Is it possible to derive pmf from a CDF with no support given?

Given a CDF of random variable, $$F_X(x)=\sum_{j=1}^x \left(\frac{1}{2}\right)^j = 1-\left(\frac{1}{2}\right)^x$$, I want to derive pmf of this random variable $X$. But there is no information about ...
• 13
92 views

393 views

### 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 ...
• 51
1k views

### 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)...
• 423
63 views

• 11
1 vote
820 views

### 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, ...
491 views

### 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 ...
• 145
80 views

### 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 ...
• 135
19 views

### 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 ...
362 views

### What is the expectation of $e^X$, where $X$ is a random variable with a geometric distribution?

if $X$ is a random variable with a geometric distribution how can I calculate $$E(e^X)$$ I have no idea on how to do that.
1 vote
168 views

### 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 $p = 1/2$...
• 171
### 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 ...