# 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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### Derivation of the expected minimum distance between uniform random variables on the unit interval

Suppose we have $n$ iid random variables, $U_1,...,U_n\sim\text{Unif}(0,1)$. What is the expected minimum distance between any two of these random points? Now, I know this has already been asked and ...
1 vote
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### Optimal strategy for uniform distribution probability game

There are 2 players, Adam and Eve, playing a game. The rules are as follows: $n$ and $d$ are chosen randomly. Adam samples a value $v$, distributed uniformly on $[0,n]$, and can either cash out $v$ or ...
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### The distribution of $XY+(1-X)(1-Y)$ for $X,Y$ sampled uniformly from [0,1]

Let $X,Y$ be sampled uniformly from the interval $[0,1]$ and $Z=XY+(1-X)(1-Y)$. I would like to know the exact distribution of $Z$. I conjecture it should be uniform as well, but was not able to prove ...
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### Hash Table and uniformly distribution

I'm trying to understand the relationship between input distributions and hash function performance in hash tables. In statistics, the theoretical probability of landing in a specific slot of a hash ...
34 views

### Probability of Christmas falling on a particular day of the week

What is the probability that Christmas (on a randomly chosen year) falls on a Monday, Tuesday, Wednesday, &c.? Accounting for the leap years and the 400-year repeating cycle, I wrote a program to ...
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### Uniform random variables with distribution over [1, 4]

2.4.2 Let W~Uniform[1 4]. Compute each of the following. (b) P(W >= 2) (c) P(W^2 <= 9) For b, I was thinking P(2<=w<=4)= (4-2)/(4-1) = 2/3. For c, I was thinking since w^2 <= 9, P(1<=...
248 views

### Uniform on $(0,1)$ vs Uniform on $[0,1]$

I read many papers about probability integer transformation or copula. Regarding the probability integer transformation, some use $X \sim U(0,1)$, and others use $X \sim U[0,1]$. What are the ...
55 views

### If $X$ is a uniformly distributed discrete random variable, what is the condition that $Y=\phi (X)$ is too?

More specifically I was solving the following problem: Let 𝑋 be a discrete random variable that is uniformly distributed over the set $S=\{−10, −9, ⋯ , 0, ⋯ , 9, 10\}$. Which of the following random ...
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### Random vector $(X, Y)$ has a uniform distribution on the unit circle. [closed]

Faced with the following problem, I do not understand how to solve this problem: Random vector $(X, Y)$ has a uniform distribution on the unit circle. Will its components be independent? It is not ...
28 views

### On the convergence in probability of the maximum statistic of a random variable according to triangular and uniform

Set up Consider the example in section 2 of Ferguson (1982). Let $X_1, \ldots, X_n$ be i.i.d. with a distribution which with probability $\theta$ is the $U(-1, 1)$, and with probability $(1-\theta)$ ...
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### Uniform distribution from Multivariate normal distribution [duplicate]

The following is from an optional exercise guide. The fact that the result should be a uniform distribution was given to me as a hint by a hasty professor, nevertheless I have been unable to solve it. ...
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### Calculating Expected Unique 2-Hop Neighbors in a Uniformly Distributed Network

In a 2D network with uniform node density $\rho$, each node has an average of $n_1 = \rho \pi R^2$ one-hop neighbors and $n_2 \leq 3 \rho \pi R^2$ two-hop neighbors. Each of these 1-hop neighbors ...
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### Density of power with random variable

Random variables X, Y, Z are independent with uniform distribution from [0, 1]. find density of $XY^{Z}$ actually I'm stuck because power is a function (Random variable). I understand how to find ...
1 vote
this question is from a interview a friend had and I was curious how to solve it. The question is: I have two random variables, $a$ and $b$. $a=rand(1,100)$ $b=rand(a,100)$ The rand function ...