# 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.

1,334 questions
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### How to transform a $U(0,1)$ variable to produce a Poisson variable?

Suppose $X$ is a uniformly distribution over $(0,1)$. How to find transformations $Y=g(X)$ to produce random variables with the Poisson distribution?
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### Finding density function of random variable

Choose an uniformly distributed random variable $U$ on the unit interval $[0,1]$. Then, what is the probability density function of $Y= \ln(U+ 1)$? I know the density function is the derivative of ...
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### How can calculate conditional pdf of Y when you dont know about f(y)

X is a uniform distribution on the interval (0,1). Y is a also uniform distribution on the interval (0,x). Its the only information that I could know. Then how can I calculate p(Y|x)? If you teach me, ...
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### uniformly distributed random variables

Ram and Shyam wanted to meet at a park about 12.30 P.M.. If Ram arrives at a time uniformly distributed between 12.15 P.M. to 12.45 P.M. and if Shyam independently arrives at a time uniformly ...
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### Frog makes two jumps (uniform distribution)

I received this problem on my exam, although I thought I answered it right, it was marked as wrong. There is a frog on a line. The frog starts from a point 0 and makes two successive jumps: first ...
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### Variance of x_i chosen from uniformly distributed hypersphere

I'm looking for an expression of the variance of a single component of a point chosen from within a uniformly distributed n-ball with radius r for any n. There are a few proofs showing that ...
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### P/1 Actuary Question: Expected value for continuous uniform distribution.

A question reads: A loss random variable has a continuous uniform distribution on the interval $(0, 100)$. A insurance policy on the loss pays the full amount of the loss if the loss is less than or ...
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### Probability mass function of $\min(X, Y)$ where $X,Y$ are i.i.d discrete uniform

Let $X$ and $Y$ be two discrete uniform i.i.d random variables distributed over $\{0, 1, 2,\ldots, N\}$. Find the pmf of $Z = \min(X, Y)$. From what I understand, I have to find the joint $pmf$ first,...
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### Combine standard normal distribution with uniform distribution

I am facing an optimization problem in my business environment that hopefully you guys can help me with. To give you some background on the topic, I am trying to calculate the inventory (called "...
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### Find probability of combination of two uniform variates [closed]

$X \sim R(0, 2)$, $Y \sim R(0, 5)$, X and Y are independent, I need to find $P(|X-Y| \leq 1)$
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### How to find critical value in uniform distribution [closed]

How do you get critical values from uniform distribution p.d.f?? this is the question I got from my teacher enter image description here
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### Tukey's symmetrical lambda distribution

U ~ Uniform(0,1) $$Z_\lambda = \frac{U^\lambda-{(1-U)}^\lambda}{\lambda}$$ I have to find the first four moments and two ($\lambda_1,\lambda_2$) such that they have the same four moments.
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### What is the distribution of the modulo of a uniformly-distributed random variable

This feels like something that's easy to answer, but maybe not. (For the record, this isn't homework from school, it's to settle an argument I'm having with a colleague.) I have a random variable $X$ ...
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### Shortcut to finding the distribution of a specific random variable

Question: A dice is rolled 3 times. Let X denote the maximum of the three values rolled. What is the distribution of X (that is, P[X = x] for x = 1,2,3,4,6)? You can leave your final answer in terms ...
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### Probability norm less than threshold in unit ball

From exercise 2.4 in Elements of statistical learning, studying this solution : http://tullo.ch/static/ESL-Solutions.pdf Points $x_{i}, i=1..N$ are uniformly distributed in a p-dimensional unit ball ...
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### How to compute a conditional expectation

I want to compute a conditionnal expectation, i know that $Z=(Z_1,\ldots,Z_p)'$ where $Z_j=\Phi ^{-1}(U_j)$ with $Z \sim N(0,R(\theta))$ and $R(\theta)$ the $p \times p$ positive definite ...
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### Generating Standard Uniform random variable

The book I am following has a problem that states: Let $U$ be a Standard Uniform random variable. Show all the steps required to generate Then proceeds to list off questions on generating other ...
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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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### An extended warranty pays a benefit of $100$ if failure occurs between time $t = 1.5$ and $t = 8$. Find $P(w<79)$.

The time until failure, $T$, of a product is modeled by a uniform distribution on $[0, 10]$. An extended warranty pays a benefit of $100$ if failure occurs between time $t = 1.5$ and $t = 8$. The ...
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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 ...
Let $X \sim uniform(0,\theta)$ we are testing $H_0: \theta = 1$ vs $H_1: \theta >1$ If we know that we reject $H_0$ if $X>0.9$ (1) find $\alpha$, the type I error (2)Suppose that $\theta=1.1$. ...