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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Uniform Distribution Min & Max unbiased estimators?

I have $n$ samples ($iid$) from a uniform distribution over $[a,b]$ with unknown $a$ & $b$, let call them $x_i$. Let $Min\{x_i\}=\hat{a}$ and $Max\{x_i\}=\hat{b}$. What are unbiased estimators ...
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1answer
33 views

Is $r_2$ a uniformly at random value in $Z_n$, where $r_2=r_1 . m$

Let $m$ be an arbitrary value in $Z_n$, where n is RSA modulo (n=p.q, where p and q are large primes). Then have: $r_2=r_1 . m$, where $r_1$ is a value chosen uniformly at random : $r_1\in Z^*_n$. ...
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10 views

orderstatistics of uniform distributions on different ranges

During a simulation I discovered an interesting phenomenon: Given you have 3 agents. 2 are uniformly distributed between [0,1] and one between [0,2]. The question is how often do the smaller agents ...
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1answer
15 views

Distributing years in a Leap Year system.

First let's take our Leap Year system: a Leap Year is a year of 366 days, as opposed to normal years of 365 days. It occurs every 4 years, except if the year is divisible by 100, and not divisible by ...
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14 views

Question about the uniform distribution and random variable operation

If I have a random variable with uniform distribution ranging from 0 to 1, as follows: $ X \sim U\left ( 0 ;1 \right ) $ And if I subtract that random variable $ X $ from 1, will the resulting random ...
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2answers
24 views

Question about probability of a random variable with uniform distribution

Why is it that when a random variable has a uniform distribution the following statement it's true? $ \Pr \left ( X_{1} \leqslant c \right ) = c $ The question arised when I was doing this ...
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1answer
52 views

Question about a sequence of iid random variables and the Uniform distribution

I will first enuntiate the question and then explain what I'm not understanding. Suppose $ X_1, X_2,\ldots, X_n $ iid with common distribution $ U(0,\theta)$. Define $M$ as follows: $ M : =\max\{ ...
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1answer
381 views

Expected Value Problem (Q-function…inside a function)

I'm working through my textbook for a communications course I'm taking, and this problem is confusing me big time. Like always, the math questions give me the most problems. Maybe I should take the ...
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30 views

Probability that one uniform distribution is less than another

I am trying to pick the variable r which maximizes an expected return. So I need to calculate the probability that $rn < x$ where n and x are both random variables with uniform distributions ...
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1answer
23 views

Is it possible to generate a uniformly distributed random 128-bit number from multiple uniformly distributed random numbers of size <= 32 bits?

If I have a uniformly distributed random number generator of up to 32 bits in length, can I generate a uniformly distributed 128 bit number by rolling my 32-bit random number generator multiple times ...
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1answer
26 views

Average distance between consecutive uniformly distributed values

Say I have a list of values $(X_1, X_2, ..., X_n)$ and $X_i$ is a uniform random variable between 0 and 1. Let $(Y_1,Y_2,...,Y_n)$ be the ordered list of those values. How do I find the expected ...
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11 views

Location, scale and location scale family

Let $X_1,...,X_n$ be an i.i.d. random sample from a continuous uniform distribution over [0,$\theta$], where $\theta>0$ is a unknown parameter. Does these random variables belong to a family of ...
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1answer
38 views

Roll a die. Are the chances of getting two same consecutive numbers the same as getting any specific random sequence?

Let's imagine a die roll. You roll the die n times. Example: I have a $6$ sided die. Assuming the distribution of the die is perfect, the chances of getting any single number are $1/6$. The ...
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1answer
81 views

About strong law of large numbers

I came across a problem: Let $X_1,X_2,...$ be independent random variables with uniform(0,1) distribution from probability space $(\Omega,\cal F,P)$. Prove that: ...
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2answers
100 views

Uniform distribution with random support

I have a uniform distribution $ X \sim U(A,B) $ where the limits themselves are random: $A \sim N(\mu_A,\sigma_A^2)$ and $B \sim N(\mu_B,\sigma_B^2)$. Hence the support of $X$ is random. $A$, $B$ are ...
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30 views

Determine the limit distribution

I have this question here that I could use some help with. Let $X_1$, $X_2$, . . . be a sequence of random variables such that $P(X_n=\frac{k}{n})=\frac{1}{n}$, for $k=1,2,...,n$ Determine the limit ...
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14 views

Standard Uniform Distibution with Random Variable

Could someone help explain how to solve the following problem: From my understanding, this problem states that we have a function, Uniform(0, 1), that will generate a random value from 0 to 1 with ...
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1answer
183 views

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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1answer
548 views

Range of Uniform Distribution

I'm trying to compute the density for the range $R_n$ for samples of a random variable $X$ that are uniformly distributed on the interval $(a,b)$. We define the range as $$ R_n = X_{(n)} - X_{(1)}, ...
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61 views

To make a polynomial with coefficients in a finite field uniform at random

We define the polynomial ring $R[x]$ consist of all polynomial with coefficients from $\mathbb Z_p$. Let $P_1$ be a polynomial such that $P_1 \in R[x]$. The aim is to compute $P_2=P_1 . r$, where ...
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Discretization of the standard uniform dist.

I need some help. Sorry for the poor use of LaTEX... a) $U_{n} = \lfloor{nU}\rfloor/n$ prove that $\lim_{n \to +\infty} {U_{n}} = U$ where $U \sim unif[0,1]$ and thus that $lim_{n \to +\infty} ...
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1answer
46 views

Uniformly at random polynomial

We have a polynomial of degree $d$, and multiply it by a polynomial whose coefficients are chosen uniformly at random and its degree is equal to or less than $d$. My question is whether the result is ...
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1answer
19 views

Exponential random variable

Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential r.v. with parameter 1/20. Smith has a used car that he claims ...
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101 views

Would Evaluating a polynomial at uniformly random points outputs random values?

I`m wondering if we evaluate a polynomial on many points picked uniformly at random. Can we say the output values Y's are uniformly at random?
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2answers
47 views

Uniform Random Number

Two uniform random numbers are chosen one after the other. what is the probability of second number second random number greater than first number? I tried this way Please correct me if I am wrong. ...
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18 views

Largest hole in uniform sampling of $m$-torus

Let $M$ be the flat m-dimensional torus $(\mathbb R/\mathbb Z)^m$ with the standard Riemannian metric. I would like to know the probability that, given a uniform sampling $X$ of size $N$, there is a ...
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1answer
230 views

Weakly bounded iff uniformly bounded in $E'$?

I have a problem: Suppose that $E$ be a normed space over $\mathbb{R}$ and $E= \{f: [0,1] \to \mathbb{R}\ \text{is continuous and such that}\ f|_{[0, \delta]}=0, \text{with}\ \delta=\delta(f)>0 ...
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1answer
64 views

Pdf for distance between two uniform random points in a circle

This is my first post in the group and I would be very thankful for any help. I am trying to develop a probability distribution for a performance analysis in my thesis. I am trying to look in to ...
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1answer
33 views

Say (X,Y) has the distribution on the area shown below find P(X>1|Y=1/2) [closed]

Say (X,Y) has the distribution on the area shown below, find P(X>1|Y=1/2)![enter image description here][1]
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2answers
81 views

uniform distribution over disk

Given two independent random variables $A$ uniform on $[0,1]$ and $B$ uniform on $[0,2\pi]$. Obtain the joint pdf, tranform to the disk, if necessary modify to obtain the uniform pdf over the disk. ...
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26 views

Let $X$ be uniformly distributed on $[0,1]$. Find the cumulative distribution function of $X-X^2$.

Let $X$ be a continuous random variable uniformly distributed on $[0,1]$. Find the cumulative distribution function of $X-X^2$. $P(X-X^2 \leq a)= P ( -X^2 + X - a \leq 0) = P ( -X^2 + X - a \leq 0| ...
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2answers
39 views

Let U and V be independent continuous random variables, identically distributed uniformly over [0,1]

Let $U$ and $V$ be independent continuous random variables, identically distributed uniformly over $[0,1]$. Show that for $0 \leq x\leq1$ , $$P(x < V < U^2)= \frac{1}{3} - x + \frac{2}{3} ...
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2answers
36 views

Uniform distribution in (0,1). P(X1+X2<=X3) and Gaussian RV with variance 1/4 and 1/9 , P(3V>=2U)

I'm appearing for a competitive examination and I find a lot of questions from probability involving $2$ or more random variables are very common. Please help me with the method on how to deal with ...
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1answer
27 views

Question on distributing weight

My question is about distributing a set of non-negative weights over a set of n items, in a way that sum of weights equals 1. For example if n=2, then w1 can be some p (where p is the probability of ...
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7 views

How can I describe uniformity in a group of values?

I have a matrix of 128x128 (6384 numerical values) referring to light intensity. I will like to know how to calculate the uniformity of the values and I am currently using the standard deviation to ...
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3answers
35 views

$X$ and $Y$ are independent and follow $U(0,1)$. Show $P(f(X) > Y) = \int_0^1 f(x) dx$

Let $X$ and $Y$ be two independent uniformly distributed r.v. on $[0,1]$, and $f$ is a continuous function from $[0,1]$ to $[0,1]$. Show that $P(f(X) > Y) = \int_0^1 f(x) dx$. I tried to prove ...
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2answers
259 views

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 $Z=X-Y$?
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76 views

Finding joint distribution function?

Let $U$ and $V$ be two independent uniform (0,1) random variables and let \begin{eqnarray*} R &=&\sqrt{\frac{U^{2}+V^{2}}{2}},\\ H &=&\frac{2U}{U+V}. \end{eqnarray*} I found the ...
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2answers
287 views

We break a unit length rod into two pieces at a uniformly chosen point. Find the expected length of the smaller piece

We break a unit length rod into two pieces at a uniformly chosen point. Find the expected length of the smaller piece
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Discrete Uniform Distribution SOA Practice Problem

X has a discrete uniform distribution on the integers 0,1,2,...n and Y has a discrete uniform distribution on the integers 1,2,3,...n. Find Var[X] -Var[Y] the answer in the book is $ ...
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30 views

The probability that uniformly distributed integers sum to a given integer

A recent CTF had a problem involving the summation of randomly distributed integers. Specifically: Consider a set $\{X_m\}$ of $M$ integers uniformly selected (with replacement) from the set of ...
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27 views

Relationship between quotient of sum of exponentials and uniform distributions

Let $X$, $Y$ and $Z$ be iid with $P(X>t)=e^{-t}$ for $t>0$. Let $U$, $V$ be independent uniform on $[0,1]$. Let $A=\min(U,V)$ and $B=\max(U,V)$. Show that $(A,B),$ and $(X/(X+Y+Z), ...
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56 views

Density of sum of two uniform random variables

I have two uniform random varibles. $X$ is uniform over $[\frac{1}{2},1]$ and $Y$ is uniform over $[0,1]$. I want to find the density funciton for $Z=X+Y$. There are many solutions to this on this ...
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1answer
31 views

Let X be a random variable with PDF fx. Find the PDF of the random variable |X| in the following

Here's my question: X is uniformly distributed in the interval $[-1,2]$. Find pdf of $|X|$... So I did P($|X| \le x$) = P($-x \le X \le x$)... From here I'm not too sure how to proceed. I know the ...
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2answers
76 views

Find the probability of $ x_2/x_3 \leq a $ where $x_2,x_3$ are uniform i.i.d.

Let $x_1,x_2,...,x_n $ be independent and identically distributed, uniformly on $(0,1)$. How to find $P(x_2/x_3 \leq a)$?
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1answer
78 views

$X$ ~ $uniform(0,1)$, $f_Y (y | X=x) = I( x<y<x+1 )$ ( for $0<x<1$ )

$X$ ~ $uniform(0,1)$, $f_Y (y | X=x) = I( x<y<x+1 )$ ( for $0<x<1$ ). Find.... a) What is the distribution of $Y$, given $X = x$? b) What is $f(x,y)$? Distribution of $(X,Y)$? c) $f_Y ...
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68 views

what is the conditional probability $P(X+Y=2|X-Y=0)$?

Consider two independent random variables $X$ and $Y$ with identical distributions The variables takes values $0,1, 2$ with probabilities $\frac12,\frac14,\frac14$. what is the conditional ...
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1answer
581 views

Distribution of Sum of Discrete Uniform Random Variables

I just had a quick question that I hope someone can answer. Does anyone know what the distribution of the sum of discrete uniform random variables is? Is it a normal distribution? Thanks!
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1answer
46 views

Help with conditional expectation

I need help finding a conditional expectation: Let $X$ be a $(0,1)$ uniform random variable i.e. $\mathbb{P}(X \in A)=\lambda((0,1)\cap A)$ where $\lambda$ is the Lebuesgue measure. We define the ...
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1answer
54 views

Expected value of the floor function of a sum of two variables

In a recently published paper I have encountered the following equality. Let $U$ be a random variable uniformly distributed in $[0,1]$ and let $Z$ be a Gaussian variable with mean zero and standard ...