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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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Joint cumulative distribution of dependent random variables [on hold]

X,Y,Z are non negative random variables which are dependent and uniformly distributed in [0,1] and let $\alpha$ be a given number in [0.1]. Now how to compute $\text{Pr}(X+Y+Z>\alpha \;\;\; \& ...
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1answer
32 views

The distribution of a posterior predictive p-value under certain assumptions

I am wondering if anyone can check my understanding of the following passage concerning posterior predictive p-values in the textbook "Bayesian Data Analysis 3rd Edition" on page 151: In the ...
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22 views

How to sample from a multivariate uniform distribution with constrained sum [closed]

Problem description: Let say that we have the following 4 uniform distributions: $u_1$~$U_1(-1, 1), u_2$~$U_2(0, 2)$, $u_3$~$U_3(0, 0.2)$ and $u$~$U[U_1, U_2, U_3]$ subject to $u_1 + u_2 + u_3 = 1$. ...
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1answer
56 views

Standard Error of a function of ML estimators

The background of the problem is as follows: Suppose $X_1,...,X_n \sim U(a,b)$ independently where $a$ and $b$ are unknown parameters and $a < b$. Let $\hat\tau$ be the MLE of $\tau$, where $\tau =...
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21 views

Check to see if sample data could be uniformly distributed

I have data and I want to see if it is plausible that it comes from some uniform distribution. Is it uniformly distributed?
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2answers
43 views

Deriving a distribution whose pdf has the shape of a square + a triangle (a right trapezoid)

I want to the derive the PDF which looks like the sum of a triangular and uniform distribution which looks like this: To do this I have simply added the PDFs for the rectangular and triangular parts, ...
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31 views

intuitive explanation for expected value of the square of a uniform variable

I'm confused about something that should be simple. Suppose I have a random uniform variable $X$ on $[0,1]$. It's fairly clear that the expected value of $X$ is 1/2. By integrating $x^2$ on $[0,1]$, I ...
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2answers
76 views

X is Uniform $[-\theta,\theta]$ what is the distribution of $Y=\frac{1}{x^{2}}$?

X is Uniform $[-\theta,\theta], \theta>0$ what is the distribution of $Y=\frac{1}{x^{2}}$ So I've been working on some transformation questions; however, most of them have been one to one. I am a ...
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2answers
106 views

Find $P(A^2 < B)$ where $A$ and $B$ are independent and uniformly distributed $\mathrm{Unif}(0,h)$, $h > 0$

I solved it two ways and in both the cases the answer is different and different from the actual answer. Approach 1: Since, $A$ and $B$ are independent, we can find the joint distribution of $AB$ ...
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2answers
71 views

Measure that takes samples that is minimized in expectation for a uniformly-distributed random variable?

I am having trouble thinking of a function that operates on a set of samples, that is, single-valued random variables between zero and one, $x_i \in (0,1), i\in\{1,2,...I\}$, and provides a measure of ...
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1answer
61 views

The pdf of a standard uniform random variable divided by constant [closed]

For a random variable $\frac{U}{a}$ where $U$ is a standard uniform random variable, I'm trying to determine the pdf. I'm not so sure what I'm getting is correct as I'm getting some funny results ...
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33 views

Bayesian classification using uniform distribution

I would like to ask you if my thought first and my answer then to the following problem is right. Suppose that I have a 3-class 1-dim classification problem where the classes $\omega_1, \omega_2, \...
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1answer
42 views

What a tests do I use to show that two parts of observations come from a two-dimensional uniform distribution?

I have a two-dimensional uniform data. I have splitted the data on two parts with a ...
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1answer
48 views

How to find an unbiased estimator of $\mathsf{Uniform}(-\theta/2,\theta/2)$

How to find an unbiased estimator of $\mathsf{Uniform}(-\theta/2,\theta/2)$. Is it a function of the order statistics?
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1answer
47 views

Transform X to get Y such that Y has a Uniform(0,1) distribution

A random variable $X$ has the PDF $f_X(x) = \frac{x - 1}{2}, \ 1 < x < 3$ Find a monotone function $u(x)$ such that the variable $Y = u(X)$ has the distribution $Uniform(0,1)$.
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1answer
77 views

Limiting distribution of a ratio using Basu's theorem

Edit: there's seems to be a typo in original question. This is a past exam question that I'm trying to solve. Suppose that $X_1,\ldots, X_n$ are i.i.d. Uniform (0, $\theta$) random variables. Let $...
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1answer
43 views

probability that matrix $2\times2$ of Random variables is Invertible

Let $X_1, X_2, X_3, X_4$ to be Variables, and let $A$ be the following matrix: $$ \left[\begin{matrix} X_1 & X_2\\ X_3 & X_4 \end{matrix}\right] $$ assume that $X_1, X_2, X_3, X_4$ are ...
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1answer
156 views

Limits of integration of a density function

My question is based on this post. In summary, $X \sim \text{Unif}(a,b)$ and $Y|X \sim \text{Unif}(a,X)$. Then the author does the following calculations: \begin{align} f(y) = \int_{-\infty}^{\infty} ...
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2answers
63 views

How to interpret the results of a chi square and p-values of a distribution uniformity test

I am reading about a method called consistent hash designed to distribute load among servers. The best case scenario would be a discrete uniform distribution where each server would get the same ...
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2answers
82 views

Convergence to a Uniform Distribution

$\newcommand{\floor}[1]{\left\lfloor #1 \right\rfloor} $ Show that if $P(X_n = i/n)=1/n$ for every $i = 1,...,n$, then $X_n$ converges in distribution to a uniformly distributed random variable $X$. ...
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1answer
81 views

Biasedness of Uniform Distribution MLE

How do I show that the maximum likelihood estimator for uniform distribution on $[0, \theta]$ for a random sample of size $n$ is biased? I've calculated the MLE as $\max_i\{X_i\}$. Intuitively, we ...
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1answer
33 views

How to specify uniform distribution with same properties as normal distribution?

What I mean is, is it possible to specify a uniform random variable $U$ with random parameters $a,b$, where $a=-b$, and are generated from some other distribution, such that the marginal pdf of $U(a,b)...
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Conditioning to derive the distribution of function of uniform random variables

After seeing this question here, I was genuinely curious if there was a way to derive this distribution. I've attempted it below using the CDF for $Z$ and conditioning on the value of $Y$. It is ...
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0answers
19 views

What is the MLE for the given uniform distribution? [duplicate]

Consider a Uniform Distribution [-a, a], with density function: p(x) = 1 / 2a Suppose you are given a dataset D = {x1, x2, x3, ... , xn} Obtain â, the MLE for the uniform distribution above with ...
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2answers
198 views

How to find distribution function of sum of 2 random variables that are uniformly distributed? [duplicate]

I am stuck with this tutorial question in one of my stats module and I would greatly appreciate some help: Let $X1$ and $X2$ be independent random variables with $a = 0$ and $b = 1$ i.e. $X1$ and $X2$...
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2answers
28 views

Getting variance of function of two uniform RVs [duplicate]

Have two independent RV's $X$ and $Y$ sampled uniformly from $[0,1]$ and $C = (X-Y)^2$. Want $V(C$). Rewrote as $V((X-Y)^2) = V(X^2) - 4V(X)V(Y) + V(Y^2)$ but that's too messy. Is it correct to write ...
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0answers
30 views

Transformation of probability distribution

I have a question about a snippet on page 526 in the PRML book of Bishop. Can someone explain to me why the right-hand side of equation (11.6) equals $z$? It's unclear to me where this derivation ...
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0answers
23 views

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
196 views

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
44 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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0answers
48 views

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
69 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
92 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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5answers
465 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
47 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
69 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
61 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
60 views

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 ...
2
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2answers
322 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
49 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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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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17 views

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
171 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
71 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
37 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
1k 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 ...
3
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1answer
121 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 ...