Questions tagged [uniform-distribution]

For questions involving random variables uniformly distributed on a subset of a measure space. To be used with [probability] or [probability-theory] tag.

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multiple distributions

Anybody can solve this question that will help me a lot. Losses due to earthquakes in a specific region are distributed uniformly in ($1MM,$5MM) and also number of earthquakes is distributed ...
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Even distribution of numbers

I'm trying to work out the most even distribution of a set of numbers across the faces of a cube. The numbers are 1-24 and I wish to place 1 number in reach corner of each face. On a standard die, ...
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Conditioning uniform distribution on subset of support gives uniform distribution

$\newcommand{\vZ}{\boldsymbol{\mathbf{Z}}}$I am reading this paper regarding a simple proof of why rejection sampling works. I managed to understand the proof of Lemma 1, but I am struggling with the ...
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Points uniformly distributed on a circle

We select randomly two points in the circumference (with length equal to 1) of a circle. Let $X,Y$ be those points (independent and uniformly distributed) and $D$ the arc distance between them. Since ...
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Pick $2$ numbers from $[-1,1]$,what is the probability that their sum is greater than $1$?

Pick 2 numbers from $[-1,1]$, what is the probability that their sum is greater than 1? It is equal to the probability that the sum of 2 uniform random variables on $[-1,1]$ is greater than 1? so ...
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Unclear “mathematical notation” in a polynomial

Although, the Enigma here is a protocol for enhancing the privacy in blockchain; however, the question is about mathematical notation, where we want to calculate the coefficients in a polynomial. In ...
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analytical distribution of the maximum likelihood estimator for a uniform distribution

Obviously the MLE of $\theta$ for a distribution $X_1, X_2, \dots, X_n \sim Uniform(0,\theta)$ is $\hat{\theta} = max(X_1, X_2,\dots,X_n)$ Now, assume $\theta = 1$. If you take repeated samples with ...
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Interpretation of sentence to pdf

Just a quick question on interpreting what this pdf looks like: Bacteria are distributed randomly and uniformly throughout river water at the rate of $\lambda$ bacteria per unit volume. n test tubes ...
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uniform distribution with interval (0,2) and sample 12

Q): Suppose that you wish to sample $12$ observations randomly from a uniform distribution on the interval $(0,2)$. An approximate value of the probability that the average of your sample will be less ...
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Given a function that generates random numbers with uniform distribution over (0, 1) find a function to generate numbers with Bernoulli distribution.

If we have a continuous random variable $X$ with uniform distribution over $(1, 0)$ we can find functions that generate numbers with other distributions using this random variable. For example if we ...
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Probability that Alice and Bob keep dating infinitely often

I solved the following problem. I would appreciate it if you can please provide feedback and let me know if I have made any mistakes. Problem statement: Online dating: On a certain day, Alice ...
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P(X>Y) when X and Y are continuous uniform distribution

Suppose $X$ and $Y$ are continuous uniform random variables. If $X \sim U[a,b]$, $Y \sim U[c,d]$ and $[c,d] \subset [a,b]$ find the probability that a random $X$ value is greater than a random $Y$ ...
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Can sum of two random variables be uniformly distributed

Say $X$ and $Y$ are two random variables where $X\in [-\alpha,\alpha]$, $Y\in [-\alpha,\alpha]$ and $Z=X+Y$. Is it possible to find two independent random variables with certain pdf (not necessarily ...
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Compute $P(X_{(2)} ≤ 3X_{(1)})$ by using the integration technique

Suppose that $X_1,X_2,X_3.X_4$ are independent $U\in(0,1)$-distributed random variables and let $(X_{(1)}X_{(2)}X_{(3)}X_{(4)})$ be the corresponding order statistic. Compute $P(X_{(2)} ≤ 3X_{(1)})$ ...
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Conditional expectation of uniform random variable given order statistics [closed]

Assume X = $(X_1, ..., X_n)$ ~ $U(\theta, 2\theta)$, where $\theta \in \Bbb{R}^+$. How does one calculate the conditional expectation of $E[X_1|X_{(1)},X_{(n)}]$, where $X_{(1)}$ and $X_{(n)}$ are ...
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Hypothesis Testing under Uniform Distribution Question

The question reads: Let $\theta > 0$ and $X \sim \mathcal{U}[0, \theta]$, i.e. $X$ is uniformly distributed on the interval $[0, \theta]$. Assume that $\theta$ is unknown, but we can observe $X$. ...
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Use the change of variables to determine the density for a uniform distribution on $[a,b]$

Knowing that the density of a uniform random variable on $[0,1]$ is: $f_{U}=\left\{\begin{matrix} 1 & x\in [0,1]\\ 0 & x\notin[0,1] \end{matrix}\right.$ How to determine the density of a ...
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Pdf of $X+Y+Z$ where $X,Y,Z$ are independent $U(0,1)$

This is my working out of the problem so far, I want to know if there is a more simpler way to solve this, or I would just be interested in other methods that one could use to solve a similar problem
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PDF of conditional uniformly distributed random variable

Given two barrels of water, $A,B$, with 1 liter each. We pour an $X\sim U[0,1]$ amount of water from $A$ to $B$ and then $Y$ amount of water randomly from $B$ to $A$ $(Y|X=x\sim U[0,1+x])$. ...
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Prove convergence of a sum of random variables

I am trying to grab on to some intuition about the area where random variables start looking a bit more like calculus. I've learned about random variables and the weak law of large numbers, but seem ...
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Average Number of users based on some condition and error calculation

I want to Calculate average No. of users selecting any particular No from random number range (2 to 6) and I have defined error condition as when more than one user selects same number. Now based on ...
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Let $X \sim (0,1)$ and $Y \sim (-1,2)$ be independent. Compute the distribution function of $Z=X+Y$ - how to break into cases?

Let $X \sim (0,1)$ and $Y \sim (-1,2)$ be independent. Compute the distribution function of $Z=X+Y$ - how to break into cases? I first found the density functions:  f_x(t) =\begin{cases} 1 &...
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The probability of sum $x+y$ to be greater than $20$

The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution.The variable $y$ takes a value between $0$ and $20$ with uniform probability distribution. The probability of ...
So I got this exercise from a book and I'm confused by a statement they made. Example: In a 100-meter Olympic race, the running times can be considered to be $U$~$(9.6, 10.0)$-distributed. Suppose ...