# Tagged Questions

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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### Probability of not choosing from a set of replaced values

The problem statement is as follows: There is a set of numbers N numbers $1..N$ (eg: N = $10^6$) N numbers are chosen uniformly and independently with replacement I would like to be able to ...
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### Find function $h$ so that $h(U,V)$ equals density of $f(a) da$ for $f(a)=\frac{1}{2}e^{-\small|a|}$, $a \in \mathbb R$

Let $f(a)=\frac{1}{2}e^{-\small|a|}$, $a \in \mathbb R$ and let $U,V$ be independant and uniform distributed on [0,1]. Now I want to find a function $h$ so that $h(U,V)$ is equal to the density ...
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### Probability density function for product and minimum of i.i.d. $U(0,1)$ random variables

If $U$ and $Y$ and $Z$ are i.i.d. $U(0,1)$ random variables, find the pdf for $A= U \times Y$ and $B = \min \{ U,Y,Z\}$.
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### Computing the distribution of a uniform r.v. with parameter being another uniform r.v.

I have this: Let $X\sim U(0,1)$, $Y\sim U(X,1)$. What is the distribution of variable $Y$? My answer: I use a geometric approach since everything happens in the square $(0,1)\times (0,1)$, see ...
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### A stick is broken into two pieces, at a uniformly random chosen break point. Find the CDF.

I'm having trouble understanding how the CDF is found in the solution below: We can assume the units are chosen so that the stick has length $1$. Let $L$ be the length of the longer piece, and let ...
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### What distribution results from drawing random numbers whose upper bound is normally distributed?

I have a normal distribution $N$ with $μ=U/2$ and $σ=U/12$ (an approximation of the Irwin-Hall distribution) which has been bounded and normalized to $[0,U]$. I will now repeatedly generate random ...
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### Formula to evenly distribute elements without knowledge of the other buckets

I am trying to write a formula to determine how to evenly distribute elements into individual buckets without specific knowledge of each bucket. The only knowledge that you have is the max number of ...
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### PMF for sum of uniformly distributed random variables

Let $X_1$ and $X_2$ be independent integer valued random variables that both are uniformly distributed on {1, 2, . . . n}. What is the PMF for S := $X_1$ + $X_2$? What I have so far: P(S=$X_1$+$X_2$) ...
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### If $f(x)$ is a strictly increasing function on the unit interval, what is the distribution of $f(\mathcal{U})$? Prove it.

$\mathcal{U}$ is distributed uniformly on the interval $[0,1]$. If $f(x)$ is a strictly increasing function on the unit interval, what is the distribution of $f(\mathcal{U})$? Prove it. Well if ...
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### Generating a Uniform R.V with specified correlation [closed]

I understand that it involves copulas, but I'm looking for a specific methodology for a specific correlation. I want to generate $U$ and $V$, random variables that are $~Uniform (0,1)$ with ...
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### Uncorrelated but not independent uniform distribution

Let $X = (X_1, X_2)$ be uniform distributed on $\{(-1,0), (1,0), (0,-1), (0,1)\}$. First of all I want to show that $X_1$ and $X_2$ are uncorrelated but not independent. Secondly I thought about ...
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### Product of exponentially distributed and uniformly distributed random variables [closed]

Let $X$ be an exponentially distributed random variable, and let $V$ be a uniformly distributed random variable on $\{-1,+1\}$ that is independent from $X$. Furthermore, let $Y = X \cdot V$. I want ...
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### Mathematics Homework 2 Question 8d :What is the probability you and your partner are now able to meet the new deadline? [closed]

You are working on a programming project with your partner for a computer science course. The project is due in 48 hours. Together, you are to produce a computer program and each of you are assigned ...
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### How do I find the cdf of $X_1 + X_2$?

$X_1$ uniform $(0,1)$ and $X_2$ uniform $(0,2)$ $$\begin{cases} f(x_1,x_2) = \frac{1}{2}, &\quad \mbox{for} \ 0<x_1<1, 0<x_2<2 \\ 0, & \quad \mbox{otherwise} \end{cases}$$ ...
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### Expected value of maximum of three random variables from uniform distribution

Three uniform random variables $X = [2.9,3.1]$, $Y = [2.7,3.1]$, $Z = [2.9,3.3]$. What is the expected value of the maximum of these three variables? $E(\max(X,Y,Z))$. I have tried to split the ...
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### Computing the probability of waiting someone - Uniform distribution

I have the following problem and I having trouble in finding it solution. I need a hint. The problem: Two people arranged to meet between 12:00 and 13:00. The arriving time of each one is i.i.d. and ...
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### Statistics $X_{(1)}$ complete for a Uniform Distribution?

Someone had asked this earlier, but since it was good practice for my qualifying exam coming up, I figured I would ask and share my work on the problem. The problem is: Suppose $X$ is ...
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### why the uniform distirbution function F(X) equal to 1 when the X is a fixed value?

I have the following quetion: Let X be a continuous random variable with distribution function $F_X(x)$ and density function $f_X(x)$. Consider the random variable Y dened by $Y = X$ if $X < a$ ...
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### Properties of the solution of a linear system with random equations

$x_i$ is drawn from $\mathrm{unif}(a,b)$, $y_i$ is drawn from $\mathrm{unif}(c,d)$. $x_i$ are independent from each other. $y_i$ are independent from each other. $x_i$ are independent of $y_i$. $i$ ...
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### approximating a uniformly distributed random variable

Suppose that $U$ is a uniformly distributed (continuous) random variable on $[0,1]$. Let's say that I am interested in finding 3 discrete points $u_1,u_2,u_3$ which approximate $U$ in some sense. My ...
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### Is the CDF of a mixture distribution uniformly distributed?

It is well-known that if $Y = F(X)$, such that $F$ is a continuous and a strictly increasing cumulative distribution function with a well-deﬁned quantile function $F^{-1}$, then $Y \sim U(0,1)$. Now, ...
Say I have a list of $n$ objects and I randomly choose one item from the list, but did not remove it. What is the method for calculating the probability I have chosen $x$ different items in the list ...