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The uniform distribution describes a random variable that is equally likely to take any value in its sample space.

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What is the distribution of (1-CDF)? [duplicate]

We know that the cumulative distribution function (CDF) follows the $U[0,1]$ distribution. What is the distribution of (1-CDF)? Is it also follows the $U[0,1]$ ? (I believe it's true for the normal ...
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1answer
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How to sample uniformly from the surface of a hyper-ellipsoid (constant Mahalanobis distance)?

In a real-valued multivariate case, is there a way to uniformly sample the points from the surface where the Mahalanobis distance from the mean of the is a constant? EDIT: This just boils down to ...
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1answer
41 views

Vector with elements from a uniform distribution, to be made unit

I have a two dimensional constant vector $\mathbf{A} = \left < 2,1 \right>$. Also, I have a vector $\mathbf{e} = \left < \epsilon_x, \epsilon_y\right >$. Both $\epsilon_x$ and $\epsilon_y$ ...
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Distance between angle distributions

I want to quantify the complexity of the street network of different cities. For each city I have the angle distribution of its streets. My hypothesis that the more complex the street network, the ...
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3answers
59 views

An oddly skewed distribution of p-values

I stumbled upon an odd result which I have difficulties to explain. In the following code, $x_1$ and $x_2$ are very similar variables. Yet the distribution of p-values for the coefficient in $x_1$ is ...
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1answer
81 views

Uniform distribution with Gaussian Priors

Let's say i've got a uniform distribution defined as follows $$X \sim U[\min (\theta_1,\theta_2),\max (\theta_1,\theta_2)]$$ I've also got that $\theta_1,\theta_2$ are i.i.d zero-mean normal ...
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402 views

If A is distributed uniformly on [8,10] and B on [9,11], what is the probability that B<A?

I was asked this question in an interview, and did not initially answer correctly though I still think my interpretation may have been the correct one. The question was: There are two delivery ...
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1answer
28 views

Convolution for uniform distribution and standard normal distribution

Consider a random variable $U$ that has a uniform distribution on $(0,1)$ and a random variable $X$ that has a standard normal distribution. Assume that $U$ and $X$ are independent. Determine an ...
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Why is the sum of probabilities in a continuous uniform distribution not infinity?

The probability density function of a uniform distribution (continuous) is shown above. The area under the curve is 1 - which makes sense since the sum of all the probabilities in a probability ...
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1answer
61 views

$X_i \sim \text{Uniform}(0, \theta)$ iid; $Y = \max{(X_1,..,X_n)}$. Why is $\theta$ necessarily larger than $y$?

I'm going through Statistical Inference by Casella & Berger, and on page 419, in the intro section of interval estimation there is the following example (note: most of the text was left out as it'...
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1answer
19 views

General rule uniform distributed classes

Given a classifier working with double values e.g. between 0 and 1. There are two classes with different ranges. Their distributions are uniform, however, one class is more likely. Is picking always ...
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2answers
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calculating correlation between binary vectors with generating with uniform distribution

I am working with some correlated binary files. I want to know, what is your opinion for calculating the correlation between binary vectors? for example, if I have two binary vectors X1 and X2 ...
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0answers
27 views

The probability of photon collision

I was reading a textbook and I couldn't figure out something that seemed really obvious: Assume that the space is uniformly and randomly filled with stars, and the mean radial distance between the ...
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2answers
294 views

What is the ratio of a N[0,1] and U[-1/2,1/2]?

I have come across a problem where I can reasonably assume that the numerator is a uniform distribution of the type U[-a,a], i.e., centered on zero, and the denominator is N[0,b]. This seems to be ...
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1answer
21 views

how to calculate the standard deviation of the sum of multiple uniform distribution

Given several independent uniform distributions, such as runif(0,5) and runif(0,50), how to calculate the sd of the sum of the two functions? And in what scenario would one needs to consider the sum ...
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0answers
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How to determine if individual is related to a given population

I would appriciate your help in the following problem: I've been told that the bonobos height is uniformly distributed, with a,b equal to [70,76] respectivly. In this group, one individual (height=70....
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0answers
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Algorithm to sample uniformily from constrained region of simplex

I want to sample uniformily from a constrained region of a simplex. The specific constraint I am interested in is the following: Sample uniformily from the set $S^{D}_\alpha$ where $$S^D_\alpha : \{...
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1answer
127 views

Sufficient statistics for Uniform (-θ,θ)

So, I know that $\max(-X_{(1)},X_{(n)})$ is a sufficient statistic for the parameter θ. But can I also say that $(X_{(1)},X_{(n)})$ are jointly sufficient for the paramether θ? In other words, can a ...
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1answer
67 views

The Distribution of max(X,1/X)

If $X \sim \text{U}(0,1)$, what is the distribution of $Y = \max(X,1/X)$? I know for this particular problem, $Y = \max(X,1/X) = 1/X$, whose distribution can be easily attained directly. However, I've ...
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0answers
33 views

Expected distance of a stone thrown into a circular pond

A stone is thrown into a circular pond of radius 1 meter. Suppose the stone falls uniformly at random on the area of the pond. The expected distance of the stone from the center of the pond is: A) $1/...
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1answer
251 views

Confidence interval for mean of uniform distribution

I've been trying to compute a 95% confidance interval for the mean of a height sample, which is uniformly distributed. I have calculated the following sample statistics: $$n=10 \quad \quad \bar{x} = ...
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2answers
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Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when drawn from a uniform [0,1] distribution?

This is an interview question for a quantitative analyst position, reported here. Suppose we are drawing from a uniform $[0,1]$ distribution and the draws are iid, what is the expected length of a ...
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1answer
86 views

Monte Carlo simulation of $\pi$

I am trying to find the value of $\pi$ using Monte Carlo simulation. However, I don't want to generate two random numbers as coordinates. Instead, I want to select a point on the edge of the square ...
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0answers
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Sufficiency and completeness of distribution

Let $X=(X_1,...,X_n)$ be drawn from the distribution with pmf $p(x_1,...,x_n)\propto \begin{cases} 1/ {\theta\choose n} & \text{if all } x_i \text{ are different and }1 \le\max(x)\le\theta \\ ...
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1answer
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Confidence interval in U(0, $\theta$)

Let $X_n = X_1, X_2,..., X_n$ be a random sample of $X \sim U(0, \theta)$, where $\theta$ is an unknown parameter. Assuming confidence level $1 — \alpha$, find confidence interval for $\theta$ where: ...
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41 views

Does two-sided UMP test exists for discrete uniform distribution?

Let $p_{\theta}(x)=\frac{1}{\theta}$ for $x=1,2,...,\theta$, where $\theta$ is a natural number. Does UMP test exists for $H_0:\theta=\theta_0$ vs $H_1:\theta$ is not $\theta_0$? I know that the UMP ...
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0answers
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The relationship between UMVUE and complete sufficient statistic

Let $X_1,...X_n$ $U(-\theta , \theta)$ I want to find the UMVUE of $\theta$ if it is exists. My answer is , there is no UMVUE in this case. Because there is no complete sufficient statistic that ...
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1answer
43 views

Convergence of sum of exponentially weighted random variables

I don't know if the title is accurate, but I have this problem: I have iid RVs $Y_k$ that has a value from {0,1,...,9} with equal probability. I need to show that $$ X_n = \sum_{k=1}^{n}Y_k10^{-k} $$ ...
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0answers
26 views

PDF for the ith ORDERED uniformly random sample compared to an evenly spaced sample

Let $r_1 ≤ r_2 ≤ ... ≤ r_N$ denote an ORDERED set of N realizations of real numbers that are uniformly random on the number line from 0 to 1. Let $R_1 < R_2 < ... < R_N$ denote a set of ...
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Generate Beta distribution from Uniform random variables

I need to generate random numbers from Beta distribution using random variables from Uniform distribution. If I have two random variables $Y_1=U_1^{1/\alpha}$ and $Y_2=U_1^{1/\beta}$, and If $Y_1+Y_2&...
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1answer
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Derivation of a truncated posterior distribution

Let $T\sim~U[-t_0,t_0]$ and let $\epsilon\sim~U[0,1]$ and $T\perp \epsilon$. We define $R=T+\epsilon$. I was trying to compute $f(T=t|R=r,T\geq t_1)$, where $t_1\in[-t_0,t_0]$ is some pre-specified ...
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1answer
31 views

Construct joint distribution of $X,Y$ such that $E[X|Y=y,y\geq \bar{y}]$ is piecewise linear

Can one construct a joint density $f(x,y)$ such that the marginal distribution of $Y\sim~U[c,d]$, no restrictions on $X$ (it would be great that $X$ also has uniform distribution) as long as it has ...
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0answers
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Marginal distribution of spherical uniform

For a random vector $\mathbf{X} \in \mathbb{R}^n$ uniformly distributed on the surface of a sphere of radius $r$, the PDF is the inverse of the surface $$f_\mathbf{X}(\mathbf{x}) = 2\pi^{-n/2}\Gamma(n/...
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1answer
31 views

The mean of the max of two uniform distributions

What is the mean of max(U(0,1),U(0,1))? Judging by computer simulations, it must be at or around 2/3, but I have no idea how to compute the precise value.
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1answer
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Finding complete sufficient statistic

Let $X_1 , ....,X_n$ be iid. $Uniform[-\theta,\theta]$. I need to find the complete sufficient statistic for $\theta$ or prove there does not exist such. I know that $T=(X_{(1)}, X_{(n)} )$ is a ...
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Uniform distribution inside Log

What is the meaning of putting uniform distribution inside log? See page 5 of this paper (Corentlin et al.) To make it more clearer, within my knowledge, I think I should put a single value inside ...
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1answer
30 views

uniform pareto system error

Let $X\sim U(0,\theta)$. Given a sample of size n, the likeliohood function is $l(\theta \mid x)=\frac{1}{\theta^n}$ Consider a pareto prior distribution $\theta\sim pareto(k,a)$ with density $\frac{...
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Clarification: Bernoulli random variable with uniform distribution

Let $Z$ be a random variable which takes the value 1 when $U \le \frac 14$, $0$ otherwise, where $U$ ~ $\text{Uniform}(0,1)$. So $Z$ is a Bernoulli random variable with PMF $$p_Z(z) = \begin{cases} p,...
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0answers
23 views

Expected value $=\infty$? [duplicate]

If we let $U_1, U_2, U_3,..., U_n$ be uniform (0,1), find $$\mathbb E[\sum_{i=0}^n iU_i^{i-1}]$$which, using the linearity of expectation, gives $$\sum_{i=0}^n \mathbb E[i U_i^{i-1}]$$ Doing this ...
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1answer
42 views

Transformation of a uniform distribution

I'm sure this is a trivial problem, but I am having trouble committing to an answer. If $U$~$(0,1)$, then $Y=-ln U$. I know that $\mathbb P(Y \le y)$ = $\mathbb P(g(X) \le y)$ =$\mathbb P(-lnU \le ...
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2answers
55 views

Uniform Density Function

As we know the uniform probability density function is f(x)=1/(b-a) if i find the density function and area of this uniform distribution between (0, 1/2) then it would be f(x)=1/(1/2-0) f(x)=2 ...
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2answers
74 views

UMVUE estimates of uniform distribution mean and width

Given are the uniformly distributed samples $$x_n \overset{\text{iid}}{\sim} \mathcal{U}\left(\mu-\frac{w}{2}, \mu+\frac{w}{2}\right)$$ for $n = 1 \ldots N$.Then the UMVUE estimates of $\mu$ and $w$ ...
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2answers
19 views

Performing a uniform crossover of parents

I'm trying to do a crossover of two vectors in my program. There are two vectors, each a parent in a sense, and they're both a series of random binary digits (1's and 0's). My goal is to randomly ...
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1answer
90 views

Expected minimum distance from a point with varying density

I'm looking at how the expected minimum Euclidean distance between randomly uniform points and the origin changes as we increase the density of random points (points per unit square) around the origin....
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2answers
516 views

Distribution of “p-value-like” quantities under null hypothesis

It is well established that p-values are uniformly distributed when the null hypothesis is true. This follows from the definition of a p-value The probability of observing a value (or more extreme ...
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0answers
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mean of product of 2 uniform random variables for values below certain threshold [duplicate]

I'm looking for the functional form to describe the mean value for all the values below a certain threshold $v$ in a distribution. The distribution is the product of two independent random variables ...
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2answers
85 views

Survival in two period game: mean of z|z<v with z=xy, x~U(a,b) and y~U(c,d)

I am looking for the functional form to describe the following: A random shock $x\sim Uniform(a,b)$ is multiplied with a second shock $y\sim Uniform(c,d)$. What is the mean value of all combined ...
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16 views

Question about normal probability plot using different data

I tried to plot different types of randomly generated data in a normal probability plot. Why is it that all data seem on the line on at least some part? The Beta(0.5,0.5) seem to follow the line very ...
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project hash into a fixed number of buckets using salt

We currently generate hashes for user-ids in our system (using md5) and bucket them into range buckets (range is 0 to 100, buckets can be 0-30, 31-70, 71-100). This process works this way - we ...
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1answer
44 views

Generate vector in $\mathbb{Z}^3$ with fixed sum and uniform distribution

I need to generate 3 discrete random variables whose sum is equal to a specified value (fixed) and is uniformly distributed, however each component of the sum has specified bounds. For example, $$ ...