Questions tagged [uniform-distribution]

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

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Maximum Likelihood Estimator of $\theta$ for U($-\theta$,$\theta$) [duplicate]

Let $X_{1}$, $X_{2}$, $X_{3}$.......$X_{n}$ be a random sample from $U(-\theta,\theta)$ distribution So the $Likelihood \ function$ is $$ L = (\frac{1}{2\theta})^{n}$$ To maximize $L$ we need to find ...
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Finding the value of $k$ for an Uniform Distribution defined on $(-k,k)$

If $X$ be an uniform distribution defined on $(-k,k)$, then the value of $k$ for so that : $$P(|X|<1) = P(|X|>2)$$ I began by defining the $p.d.f$ of the Uniform function namely: $$ f(x) = \...
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Finding the MLE of Uniform distribution [duplicate]

Let $x_{1} = 2.4$ , $x_{2} = 9.2$ , $x_{3} = 5.2$ , $x_{4} = 4.1$ , $x_{5} = 2.1$, $x_{6} = 3.1$ be the observed values of a random variable of size 6 from the uniform distribution with parameters $(\...
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Difference of dependent uniform random variables [closed]

My question is similar to the one posed here for a sum of dependent uniform RVs. How can I find the CDF of $T=X-aY$, where $X\sim U[0,B]$, $Y\sim U[0,X]$, and $a<1$ is a constant. I've tried ...
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How to calculate the distribution of the sample mean of uniform distribution? [duplicate]

I am working on the following question but I'm not sure if my approach is correct. Given that X~U(4,8), I need to find the distribution of the sample mean for a sample size 30. My approach is that ...
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Defining a measure of uniformity that finds the most "uniform structure" for the most cases of countably infinite sets? [closed]

I am temporarily banned from math stack exchange but I believe this is a statistical question. If not, wait till the ban is over in 10 days then transfer it to math stack exchange. Question I want to ...
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Probability of limit of discrete uniform r.v

Let $\mathrm{X}_{\mathrm{1}}=1$ and $\mathrm{X}_{\mathrm{i}}, 1<\mathrm{i}\leq\mathrm{N}$, be $\mathrm{N}$ independent and uniformly distributed random variables over the set $\{1 / \mathrm{i}, 2 / ...
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Is a uniformly random number over the real line a valid distribution?

Is $\text{Unif}(- \infty, \infty ) $ a valid distribution? I'm trying to capture the idea of a completely random number (where every number has an equal chance of being chosen), but I'm not sure if ...
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Sum of the two or more non-standard uniform distribution? [duplicate]

Can anyone show the sum of two $U(-1,1)$? Any statistical methods to solve the sum of three and more $U(-1,1)$? I am doing a uniform random walk simulation. Can simulate using coding not can not ...
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Most Powerful Lower Tail Test for Uniform Distribution

Problem Statement: Let $Y_1, Y_2,\dots,Y_n$ denote a random sample from a uniform distribution over the interval $(0,\theta).$ Find a most powerful $\alpha$-level test for testing $H_0:\theta=\theta_0$...
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Sampling from a multivariate gaussian via affine transformation of uniform random samples?

I saw a proof some number of months ago and seem to have forgotten to bookmark it. Essentially, the proof showed that with just a few elements, the {mean vector, cov vector} of the target gaussian and ...
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Find the probability density function of $Y = X_1 + X_2$ [duplicate]

Suppose that $X_1$ and $X_2$ are i.i.d random variables and that each of them has a uniform distribution on the interval [0,1]. Find the probability density function $Y = X_1 + X_2$ I understand that ...
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Density of min(X,Y), max(X,Y) for iid Uniform (Related to other post)

I was looking at Determine density of $\min(X,Y)$ and $\max(X,Y)$ for independently uniform distributed variables There's a very detailed answer, but while I was doing the same exercise by myself I ...
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Bivariate Distribution with Uniform Marginals is Bound to be Uniform?

If $X\sim U , Y\sim U$ , and $X,Y$ may be non-independent. Can we say the joint distribution of $X,Y$ is uniform?
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Probability that any element of a random unit-length vector is large [closed]

Given a vector $X \in R^n = \{x_1, x_2, ..., x_n\}$ drawn uniformly such that: $x_i \in [0, 1]$ for all $i$; and $\sum x_i = 1$, how would you find the probability that any of the $x_i > y$, for ...
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How to determine the likelihood a random number generator is using a uniform distribution?

Let's say I have a blackbox function generate_number() that generates a random number between 1-N; and assume N is known. Each ...
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Earliest Deviation from uniform distribution [duplicate]

How can I to compute the earliest deviation from a uniform distribution from a heavy tailed distribution.I find that one can do it as follows: max_ix = np.argmax(np.cumsum(hist) - np.sum(hist)*bins[1:]...
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If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$? [closed]

If $20 $ random numbers are selected independently from the interval $(0,1) $ what is the probability that the sum of these numbers is at least $8$? I tried to take this question https://math....
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How to compute the PDF of a conditional distribution [duplicate]

Let $T \sim Unif(0, 1)$. Then, $f_T(t) = 1 \text{ for } t \text{ in [0, 1] (0 elsewhere)}$. How do we formally compute $f_{T \mid T > 0.5}$? Intuitively, $f_{T \mid T > 0.5}(t) = 2 \text{ for } ...
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Simulate drawing marbles from a bag with replacement time efficiently

I have a bag with 256 marbles, each a different color. Everytime I run the experiment, I have a 1/16 chance of drawing any marble. I can simulate this by instead considering a bag with 16×256 marbles, ...
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Testing for circular uniformity of headings (Rayleigh, v-test)

I have two-dimensional recordings of animal trajectories. The animals exit their nest and I am trying to test whether their headings over a period of time have a distribution different than uniform. ...
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Self-study: Comparing Uniform and Normal CDF/quantiles for a given range

Not sure if the title is perfect. Nevertheless, there are two persons drawing $\alpha$. ‘A’ draws from $N(0,1)$ and ‘B’ from $U(-2\sqrt{2\pi}, 2\sqrt{2\pi})$. For which person is it more likely that ...
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Expectation for the MLE for a Uniform Discrete Random Variable

$\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$ Problem Statement: Suppose that $n$ integers are drawn at random and with replacement from the integers $1,2,\dots,N....
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Likelihood calculation w.r.t. uniform discrete distributions

I am working on a little project where I use observations to infer a hidden parameter in Pokemon battling. Without delving into the the mechanics too much, I will attempt to describe the context of ...
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Test whether $n$ distinct balls are distributed uniformly into $m$ bins

Suppose I have $m$ bins and $n\gg m$ balls, labelled $1,\dots,n$. The balls are placed into the bins with an unknown distribution. I now want to verify that the balls are most likely distributed ...
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Construct a random variable uniformly distributed around a value from another uniform distribution [closed]

Consider a continuous random variable $H$, uniformly distributed over range $[1,2]$, i.e. $H\sim U(1,2)$. Someone draws $h^*$ from $H$. Consider now a value $h'=h^{*\gamma}c\;(\gamma<1)$ , where $c$...
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Maximum Likelihood and the Empirical Distribution

I am reading Goodfellow et al. "Deep Learning" book (2016). In chapter 5, where they are explaining Maximum Likelihood, they imply the empirical distribution $\hat p_{data}$ as a uniform ...
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Find a Confidence Interval for Data from a Uniform Distribution on $(\theta-.5,\theta+.5).$

Let $X_1,...,X_n$ be a random sample on $\text{Uniform}(\theta -1/2, \theta +1/2).$ I need to find a confidence interval for $\theta$ with ($1-\alpha$) of confidence. I have this: $\max(X_i)-1/2<\...
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Probability distribution of the distance of a point in a square to a fixed point

The question is, given a fixed point with coordinates X,Y, in a square of size N. What is the probability distribution of the distance to a random point. More specifically, what is the probability ...
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different answers to uniform probability on a disk question

why are the answers to a. and to b. different? There is .25 probability that a point will be within r/2 of the center, just by calculating the ratio of the areas of the two circles. Why is .25 not ...
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Generate batches of random numbers that each are zero-sum and for which mean of the absolute values is uniformly distributed over specified interval

In the context of polls of voting results, I want to generate random numbers with specific properties to sample the possibilities within the margin of error of the poll. For example, suppose I have ...
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Testing which of two distributions deviates more from the uniform distribution [closed]

I'm running an experiment, and am unsure what statistic I should be using for my key test. The design: People are instructed to privately use a random number generator to generate a random number (1-6,...
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computing $P\left(\max(U_{(1)}, U_{(2)}-U_{(1)}, \cdots,U_{(n)}-U_{(n-1)} ) <a\right)$

Let $U_{1}, \, ... \, ,U_{n}$ be a random sample of uniform random variables $U_i \sim \mathrm{Uniform}(0,1)$. Let $U_{(1)}, \, ... \, , U_{(n)}$ be the order statistics of the sample. My problem is ...
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Probability of facing a specific number when having N random numbers from a "discrete uniform distribution of N numbers"

What I know: with R as a random variable from a discrete uniform distribution of 1000 numbers [1, 1000]. there is a 1/1000 chance to have R=123 (or any other number in [1, 1000]) What I think I know: ...
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Covariance matrix of multivariate Gaussian distribution

I have a Gibbs Sampling problem in which to sample the initial values of [x] variables where x=[x1 x2 x3 x4] represented by Multi variate normal distribution: It is given that each element of [x] has ...
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Finding the distribution of X-Y if X and Y are iid uniform (-a,a) [duplicate]

Suppose X and Y are independent and follow uniform distribution (-a,a). How do we find the distribution of X-Y? I tried finding the area with the help of a diagram for cases when x-y>0 and x-y<0....
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How can one find $g$ so that the test will have size $\beta$ for the following uniform distribution case?

I have the random sample $X_1, X_2, \dots, X_n$ drawn from the uniform distribution on $[\varphi, \varphi + 1]$. To test the null hypothesis $H_0 : \varphi = 0$ against the alternative hypothesis $H_1 ...
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Convergence of uniformely distributed random variables on a sphere

I am reading "Asymptotic Statistics" by A.W van der Vaart and I am stuck with an exercise of chapter 2. Here is the question : for each $n \in \mathbb{N}$, let $U_n$ be uniformly distributed ...
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How to see that this is a mixture of the uniform and Erlang?

I have a pdf in a form: $$f(x) = \begin{cases}\frac{1}{2} + \frac{1}{2} \frac{\lambda^k x^{k-1} e^{-\lambda x}}{k!} & \text{for $0<x<1$} \\ \frac{1}{2} \frac{\lambda^k x^{k-1} e^{-\lambda x}}...
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How was the law of total probability used here for this conditional probability to get this result?

If $X(t)$ is observed at a random time $U \sim \text{Uniform}(0, 1)$, then, by the law of total probability, we have that $$P(X(U) = k \mid X(0) = 1) = \int_0^\infty P(X(u) = k \mid X(0) = 1) g_U(u) \ ...
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Bounding maximum inner product out of $n$ randomly sampled unit norm vectors

Let $w \in \mathbb{R}^d$ have unit norm and $x_1, ..., x_n \in \mathbb{R}^d$ be $n$ randomly sampled vectors from the uniform distribution over the $d$-dimensional unit sphere. Can one obtain a lower ...
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Testing on uniform distribution with large sample?

Let $$X_1,X_2,\dotsc,X_n$$ be a random sample from U(0, a) and $$ Y_1,\dotsc,Y_n$$ be a random sample from U(-a,a) a is natural number. Let $$H_0$$ a is even and $$H_1$$ a is odd. On the basis of $$...
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Applying Wilks' theorem to uniform distribution

Suppose $X_i $ ~ $ U(0,b)$, for $i=1,2...n$ and we want to test the null hypothesis that $b=1$. Assume $H_0$. Then from Wilks' theorem, as $n \rightarrow \infty $, $ 2\ln(\frac{L_x(H_1)}{L_x(H_0)})$ ...
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understanding uniformly distributed success probability

I'm currently reading a theoretical economics paper, where they used an example I don't quite understand. I hope you guys can help me out🙂 The following excerpt is the example I don't quite ...
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minimum distance estimation

I need to set up a minimum distance estimator for the uniform distribution $U[0,\theta]$ and take the $\mathcal{X}^{2}$ statistic as distance https://en.wikipedia.org/wiki/Minimum-distance_estimation $...
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Marginal distribution of uniform distribution over sphere

Let $(x_1,…,x_n)$ be a random vector uniformly distributed on the $n$-dimensional unit sphere. Is there a closed form solution for the joint distribution of $P(x_1, x_2)$?
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Cumulative Distribution Function of $S_{N_{t}}$ where $S_{N_{t}}$ is the time of the last arrival in $[0, t]$

I am confused on this problem. My professor gave this as the solution: $S_{N_{T}}$ is the time of the last arrival in $[0, t]$. For $0 < x \leq t, P(S_{N_{T}} \leq x) \sum_{k=0}^{\infty} P(S_{N_{T}}...
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Posterior distribution of two i.i.d. uniform r.v. given their difference with graphical intuition

I have two i.i.d. random variables, $\theta_1$ and $\theta_2$ which are uniformly distributed on the unit square. I need to compute the joint posterior distribution of these two variables, given their ...
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Show that the maximum of $x_1,...,x_n \sim \mathrm{Uniform}(0,\theta)$ is a sufficient statistic for $\theta$. (From definition)

Problem Show that the maximum of $x_1,...,x_n \sim \mathrm{Uniform}(0,\theta)$ is a sufficient statistic for $\theta$. Background This question has been asked before, but most answers tackle the ...
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1answer
56 views

Number of samples required to have visited all classes of a uniformly distributed distribution?

So let's say I have a set of binary vectors $x \in \{0,1\}^n$. Hence, $|\{x\}| = 2^n$ . For all $x$, there is a class $c_i$. We do not know what is this class a priori, but we can compute it once we ...

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