Questions tagged [uniform]

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

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1answer
132 views

For the case of Pokemon IV, what distribution is it for the percentage value?

I took statistics some 25 years ago, and remember that if students take a test, then the test scores actually form a bell curve. But somebody claimed that for Pokemon IV: a random number from 0 to 15 ...
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2answers
826 views

Normal Distribution with Uniform Mean

I'm trying to understand the distribution, mean, and variance of a normal random variable, with the mean parameter having a uniform distribution. Based on my R simulations it seems that this compound ...
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0answers
904 views

Finding UMPT for uniform distribution with varying support

$\textbf{Problem}$ Let $X_1,\dots,X_n$ be a random sample from $f(x;\theta) = 1 / \theta$, where $0 < x < \theta$. We want to test $H_0: \theta \leq \theta_0$ versus $H_1: \theta > \theta_0$. ...
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1answer
705 views

Generate random numbers from “sloped uniform distribution” from mathematical theory

For some purpose, I need to generate random numbers (data) from "sloped uniform" distribution. The "slope" of this distribution may vary in some reasonable interval, and then my distribution should ...
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2answers
413 views

How is the spherical elevation angle distributed when $(x,y,z)$ are uniformly and normally chosen?

As a follow up to How the polar coordinate, $\theta$, is distributed when $(x,y) \sim U(-1,1) \times U(-1,1)$ and if $(x,y) \sim N(0,1)\times N(0,1)$? Assume $(x,y,z) \sim U(-10,10) \times U(-10,10) \...
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2answers
312 views

Expectation of 2 functions with one random variable

This may be a trivial question but I want to consult with you all. Let U be a continuous random variable taking values int he interval [0,2pi]. Let X = cos(U), Y = sin(U). Determine the Pearson ...
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1answer
329 views

Is there a parametric joint distribution such that $X$ and $Y$ are both uniform and $\mathbb{E}[Y \;|\; X]$ is linear?

Is there a parametric joint distribution such that $X$ and $Y$ are both uniform on $[0, 1]$ (i.e. a copula) and $\mathbb{E}[Y | X = x]$ is linear (by which I mean affine) in $x$? That is, $$\mathbb{E}...
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1answer
291 views

Discrete uniform distribution on a finite set

I have a random variable Y which has a discrete uniform distribution on the set {-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}. I have to find the following: i) Find P(Y) ii) P($Y^2$)? iii) E($Y^2$) Answers:...
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1answer
353 views

Distribution of the predictors in GLM

I am using a GLM to model my data. The response variable is binary and I have three predictors of which two are continuous variables and one is binary. Would the distribution of predictors be ...
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0answers
143 views

Distribution of X-U(0,1) conditioned on sigma algebra of Y/X, where is Y is U(0,1)?

The question I have is: Define X,Y to be two independent uniform(0,1) random variables and $Z:=\frac{Y}{X}$ Compute $P(X<x|\sigma(Z))$ The answer given apparently by "straightforward elementary ...
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Why is generating 8 random bits uniform on (0, 255)?

I am generating 8 random bits (either a 0 or a 1) and concatenating them together to form an 8-bit number. A simple Python simulation yields a uniform distribution on the discrete set [0, 255]. I am ...
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1answer
36 views

Finding P(U <4) where U is uniformly distributed with known mean and variance

I have been given a question: if U is uniformly distributed with mean 5, and variance 3, what is P(U<4)? This is all the information that has been given. I'm ...
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1answer
57 views

order statistic (random sample from U(0,1) )

for a random sample $X_1 , X_2 .... X_5$ , from a Uniform (0,1) , isn't the distribution of median (say y) be given by $$ f(y)= \frac{y^2 (1-y)^2}{\beta (3,3)}\,,\qquad 0 < y < 1 $$ this can ...
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Test for uniformity in R

i am searching for a test for uniformity in R. ks.test(x,'punif') looks quite good, but my data has only 6 different values (results of rolling a die) which leads ...
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3answers
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How is $\theta$, the polar coordinate, distributed when $(x,y) \sim U(-1,1) \times U(-1,1)$ and when $(x,y) \sim N(0,1)\times N(0,1)$?

Let the Cartesian $x,y$ coordinates of a random point be selected s.t. $(x,y) \sim U(-10,10) \times U(-10,10)$. Thus, the radius, $\rho = \sqrt{x^2 + y^2}$, isn't uniformly distributed as implied by $...
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1answer
501 views

Maximum gap between samples drawn without replacement from a discrete uniform distribution

This problem is related to my lab's research in robotic coverage: Randomly draw $n$ numbers from the set $\{1,2,\ldots,m\}$ without replacement, and sort the numbers in ascending order. $1\le n\le m$...
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1answer
65 views

Testing if measurement comes from complex distribution (uniform plus normal)

I want test if measurement comes from my reference. I know reference distribution, for example it is: $$ X = f(A,B) \\ A \sim N(0, \sigma) \\ B \sim U(a,b) \\ $$ $ f(A,B) $ - some function of the ...
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How to check the correctness of calculations with a gamma distribution?

I’m reading Ponomareva, Roman, and Date (2015) and trying to generate vector $P$ of the $2Ns + 3$ probability weights: $$P =\{\underbrace{p_1, p_2, \ldots, p_s, p_1, p_2, \ldots, p_s,p_1, p_2, \ldots, ...
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How to measure the asymmetry of data distribution in a convex?

I have some 2d points data and I generated a convex hull mesh. Looking by eye, it seems that the points are not uniformly distributed inside the convex. I wonder what is the best way to characterize ...
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138 views

Characteristic function of uniform random variable [duplicate]

I am trying to find out expectation of a function of a uniform random variable. I am given a random variable $x$ that is uniformly distributed over the interval $[0, a]$. I want to find out the ...
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1answer
347 views

Probability density of compound triangular distribution with uniformly distributed mode?

What are the probability density function and cumulative distribution function of a compound triangular distribution with uniformly distributed mode, both supported on $(-a, a)$? I.e., $$ m \sim \...
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141 views

Check that a statistic is complete

I have a question regarding completeness of a statistic. So the problem is: $n$ numbers are chosen randomly and independently between $a$ and $b$ ($0 < a < b$) but the information about $a$ and ...
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0answers
66 views

How to get Normal(Gauss) distribution from unifrom distribution? [duplicate]

I need to use rand(uniform distribution) function in matlab to generate a gaussian/normal distribution. What is the best way to do this?
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Why does the L2 norm heuristic work in measuring uniformity of probability distributions?

To start off, please go through this question regarding measuring non-uniformity in probability distributions. Among several good answers, user495285 has suggested a heuristic of simply taking the ...
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1answer
231 views

How to randomly sample values given the extremly small and large log-probabilities? [duplicate]

Assume a long list of log-values. The list consists of very small negative numbers, very large negative numbers, as well as very large positive numbers. To avoid numerical overflow/underflow, I need ...
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2answers
94 views

uniform distribution: expectation of sum squared observations

I'm trying to follow ML lesson about Bayesian inference. They have a sample of n observations from a uniform distribution: $x_i = U(0, \theta)$. They claim that $E[(\sum x_i)^2] = n(n-1)\theta^2/4 +...
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1answer
106 views

uniform distribution - computing the squared error for an estimator?

Background: I'm trying to follow ML lesson about Bayesian inference. They have n samples from a uniform distribution $U(0, \theta)$, and they suggest 2 estimators: 2 times the average $2\frac{\sum{...
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1answer
303 views

Is the sum of two independent non-overlapping uniforms uniform?

Suppose $X_1\sim U[a,b]$ and $X_2\sim U[c,d]$ with $a<b<c<d$ and suppose they are independent. I guess that the sum must be a uniform but I don't know how to show it [EDIT: I was wrong]. I ...
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1answer
169 views

Simplest possible (uniform) sampling of the interval [0,1] with n points

The simplest possible sampling of a function in the region [0,1] for the purpose of finding the area under the curve, for instance, could be just take the left offsets of the bars. That is, you have ...
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1answer
174 views

pyMC produces values outside range of uniform distribution while sampling from Bayesian hierarchical model [closed]

I have a hierarchical Bayesian model consisting of a Uniform prior distribution, between a minimum and maximum value (hyperparameters) at the top level of the hierarchy. I sample a "mean" from the ...
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2answers
447 views

Order statistics for non i.i.d. variables

$u$ is a random variable with uniform distribution in $[a,b]$ and is not observed (the distribution is known though). At every period $t \in \{2, ..., T\}$, the researcher observes $Y_{t+1} = \alpha ...
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1answer
2k views

Find posterior distribution for uniform distribution

Given X with uniform distribution in the interval [μ,μ+θ]. Suppose θ is given. Find the posterior distribution with prior distribution on your own. From that, find the Bayesian estimator with ...
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1answer
4k views

Generating random numbers from normal distribution via inverse uniform distribution

I would like to create a random number generator for the normal distribution via using a uniform linear congruential generator (on uniform distribution) and the inversion method. However, I'm getting ...
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245 views

Simulate sampling K values from uniform distribution with replacement

I am trying to reformulate sampling k values from a uniform distribution with replacement as a problem on deciding whether or not the nth value should be included in the sampled set. In other words, ...
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2answers
20k views

From uniform distribution to exponential distribution and vice-versa

This is probably a trivial question, but my search has been fruitless so far, including this wikipedia article, and the "Compendium of Distributions" document. If $X$ has a uniform distribution, does ...
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0answers
108 views

Is the Gaussian distribution the only statistical distribution fully determined by the mean and variance?

I've read that the Gaussian marginal is fully determined by the mean and variance. What does this mean in reality? If we consider a Gaussian marginal PDF is given by $$ \pi_G(\xi|\mu,\sigma) = {1\...
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1answer
101 views

Expectation and variance of Uniform Distribution

If X is uniformly distributed over (0,1),I want to calculate $E[X^2],E[X^n]$ and $Var[X^n]$ Answer:I tried to get 2nd derivative of mgf $\frac{e^{tb}-e^{ta}}{t(b-a)}$ to compute $E[X^2]$. I tried ...
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2answers
103 views

Do the data from these two different samplings follow the same distribution?

I have two approaches for data sampling: Sampling from a uniform distribution in $[0, 1]$ and rejecting values outside a certain limit, i.e. $0.50<p<0.51$. Sampling from a uniform distribution ...
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2answers
298 views

The distribution for the Kronecker product of two uniform random vectors in unit sphere?

Suppose that two random vectors $x$ and $y$ are uniformly distributed on unit sphere $S_{n-1}$. Is it possible to show that the Kronecker product of $x$ and $y$ is uniformly distributed on a subset of ...
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2answers
1k views

Conditional Distribution of uniform random variable given Order statistic

I have the following question at hand: Suppose $U,V$ are iid random variables following Unif$(0,1)$. what is the conditional distribution of $U$ given $Z:=\max(U,V)$ ? I tried writing $Z=\Bbb{I}\...
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1answer
453 views

Bayes Rule Uniform Distribution

For Bayes rule, if my likelihood, and prior distribution are both uniform, is my posterior distribution also guaranteed to be uniform? In addition to this, if I apply some transformation to a ...
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1answer
143 views

Easier way to find $\mathbb{E}\left[X_{(2)}| X_{(1)}, X_{(3)}\right]$?

Consider 3 iid samples drawn from the uniform distribution $u(\theta, 2\theta)$, where $\theta$ is parameter. I want to find $$ \mathbb{E}\left[X_{(2)}| X_{(1)}, X_{(3)}\right] $$ where $X_{(i)}$ ...
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1answer
49 views

Is it possible, practically, to sample any point on 0 to 1 under Uniform sampling?

I am solving optimization problems where I am trying to find the minimum of a function over some sample space $\mathcal{X}$, i.e., $\min\,f(x):x\in\mathcal{X}$. Now the optimization algorithm I am ...
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0answers
2k views

When should I use the Normal distribution or the Uniform distribution when using Xavier initialization?

Xavier initialization seems to be used quite widely now to initialize connection weights in neural networks, especially deep ones (see What are good initial weights in a neural network?). The ...
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3answers
365 views

Given $X,Y\sim i.i.U[0,1]$, what is $P(X<Y)$?

Let a, b be real numbers randomly selected independently and uniformly from the range of (0,1). What is P(a < b)? The problem here is that a can be equal to b, so is P(a < b) ≈ 0.5 or P(a ...
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1answer
540 views

Standard deviation of the sum of a discrete uniform

If I randomly generate a number between 1 and 10.... 10 times, and then total all the numbers, what will the standard deviation of that total be? I'm pretty sure the mean of the total will be 55.5, ...
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1answer
93 views

Expected root of quadratic random polynomial

Suppose $A,B,C$ are i.i.d. random variables with uniform distribution on $[-1,1]$. I'm interested in the expected roots of the polynomial $Ax^2 + Bx + C$, which are complex random variables given by $$...
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1answer
346 views

Improving Chebyshev-type bound for discrete uniform distribution

I take $N$ samples from a fully specified, discrete, finite uniform random variable $X$ with mean $\mu$ and variance $\sigma_X^2$. I want to find the probability that the absolute error of the ...
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2answers
495 views

How to efficiently choose $n$ subset out of a set of $m$ many numbers, in a randomized uniform manner?

Problems: It is fairly simple: we have a list of numbers $x_1, x_2, \ldots,x_n,\ldots, x_m$. Our goal is to randomly and uniformly choose a subset of $n$ many numbers out of these. This means that, ...
4
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1answer
43 views

Distribution of Max of 2 Uniforms with different support

I've got 2 independent draws from these two distributions :$X\sim U(0,1)$ and $Y\sim U(0,2)$. I want to find $E(\max(X_,Y))$. I know that for two (0,1) independent Uniforms: $P(\max(X,Y)<z)=P(...