# 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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### Unclear “mathematical notation” in a polynomial

Although, the Enigma here is a protocol for enhancing the privacy in blockchain; however, the question is about mathematical notation, where we want to calculate the coefficients in a polynomial. ...
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### Prove the maximum order statistic $X_{(n)}$ is a minimal sufficient statistic for the uniform$(0,\theta)$ family using a particular theorem

I'm doing Exercise 6.26 in Casella and Berger's Statistical Inference, and I'm trying to prove the following: "Use Theorem 6.6.5 to establish that, given a sample $X_1,...,X_n$, the maximum order ...
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### Discrete uniform vs binomial distribution

Situation: a box contains N balls numbered $1,2...,N$. $N$ unknown. $n$ balls drawn using SRS with replacement and number recorded. A random variable $X$ is defined as the number recorded on $ith$ ...
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### Expected outcome of a process following a uniform distribution [closed]

A gambler is playing a game of roulette. There are $37$ possible outcomes, each numbered from $1$ to $37$. The probability of rolling any outcome is the same for each outcome. One game of this ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 $X$. ...
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 ...