For questions involving random variables uniformly distributed on a subset of a measure space. To be used with [probability] or [probability-theory] tag.
Questions tagged [uniform-distribution]
2467 questions
5
votes
4 answers
The One-way Highway
This is supposedly a thought-provoking interview question asked, and I though I have an idea of a possible solution, I can't prove it.
The question is the following:
You have $n$ cars that are all traveling the same direction on an infinitely long…
Neil
- 446
2
votes
2 answers
Uniform Distribution Problem
Let $X$ be a random variable uniformly distributed in $[0,1]$, and let $Y$ be a RV uniformly distributed in $[X,1]$. I want to calculate the theoretical distribution of $Y$, any hints? I already tried with simulation, which gave me an idea of what…
John
- 33
2
votes
1 answer
Simulate the results of rolling a die using Uniform[0, 1]
I saw this question in one of my textbooks:
Let U be a random variable having a uniform(0,1) distribution. Describe how to simulate the outcome of the roll of a die using U.
I know that the outcome of rolling a die follows discrete uniform…
Paul726
- 23
2
votes
1 answer
Are the fractional parts of multiples of an irrational number by elements in an arithmetic progression dense in $(0,1)$?
Assume that $a$ and $b$ are positive integers, and consider the arithmetic progression $\{{s_n}=(an+b):n=1,2,3,\cdots\}$. Let $\alpha$ be an irrational number, and consider the fractional part ${r_n} = \{{s_n}\alpha \}$ defined by $${r_n} =…
student
- 1,324
2
votes
2 answers
Combining two identical uniform distributions
Say two random variables, $X$ and $Y$, are such that $X$ ~ $U(0,a)$ and $Y$ ~ $U(0,a)$.
What will the pdf be for $Z$, where $Z=X-Y$?
Ben
- 21
2
votes
1 answer
Find the limit joint distribution of the random vector uniformly distributed in the ball
Given an integer $n \geq 1$, define $\left(X_{1}^{(n)}, X_{2}^{(n)}, \ldots, X_{n}^{(n)}\right)$ as a random vector uniformly distributed in the ball
$$
\left(X_{1}^{(n)}\right)^{2}+\left(X_{2}^{(n)}\right)^{2}+\cdots+\left(X_{n}^{(n)}\right)^{2}…
2
votes
2 answers
Distributing 6 persons in their shifts evenly with rotating partner
I thought this was easy but I was mistaken.
I need to make a schedule for 6 persons. They have to make shift by two (partner) but the partner should also rotate so that all person gets to be partnered with everyone else.
The first set was…
Wayne
- 123
2
votes
2 answers
Prove that a function is uniformly continuous
This is my question :
Let $f$ be defined on an interval $I$, and suppose there exists an $M>0$ and $\alpha>0$ such that
$$
|f(x) - f(y)| \leq M|x -y|^\alpha,
$$
for $x,y \in I$. Prove that $f$ is uniformly continuous on $I$. If $\alpha>1$, prove…
david
- 69
2
votes
1 answer
First two events out of twenty which are distributed uniformly
This is not a homework question but something that occured to me while studying for an examination. Is there a "shortcut" way of calculating this?
There are $20$ independent uniform random variables, each denoting an event, $X_i $ ~ $ U(0,1)$ for…
TheNotMe
- 4,841
1
vote
1 answer
Method of moments on uniform distributions
I need help on how to find the estimates $a$ and $b$ in the uniform distribution $\mathcal U[a,b]$ using the method of moments.
This is where I am at:
I have found $U_1=\overline X$ and $m_1=\frac{a+b}2$ Also, $m_2=\frac1{n(E(X_i^2)}$ and…
Bree
- 203
1
vote
1 answer
Looking for a simple bivarate uniform distribution with non-zero covariance matrix
Obviously there are many forms this can take, I'm looking for on that gives an non-zero (off diagonal elements) covariance matrix. Does anyone know of one?
user2350366
- 513
1
vote
1 answer
spin arrow of random variables
Spin an arrow attached to the center of a circular board, let theta be the final angle of the
arrow, theta<= 2pi. The probability that theta falls in a subinterval (0, 2pi] is proportional
to the length of the subinterval. The random variable is…
Jaswanth
- 19
1
vote
1 answer
Uniform distribution problem of finding overlapping region
I found $\displaystyle \int_{5}^{15}\dfrac{dx}{22}$
Can somebody just verify is it correct?.
Upstart
- 2,613
1
vote
0 answers
Balanced distribution of resources
Let's say we have 9 storage units with the following current quantities:
152, 153, 154, 159, 157, 147, 140, 265, 205.
The 9 storage units will be supplied daily, for 30 days, with the following daily maximum quantities:
day 1: 12, day 2: 13.5, day…
Overmind
- 121
1
vote
1 answer
distribution of intervals of samples of a distribution
I have a uniform random variable $X \sim \mathcal{U}(a,b)$ and I take a sample of $N$ i.i.d. realization from it: $\{X_1, X_2, ..., X_N\}$. I'm interested in the statistics of the interval between every two successive realizations after they are…
subset
- 65