# 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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### For which value of $i$ is $p_i$ the largest? [closed]

Suppose $X$ is distributed uniformly on $(−1,1)$. For $i = 0, 1, 2, 3$, let $p_i = P\bigg(X^{2} \in \bigg(\frac{i}{4}, \frac{i+1}{4}\bigg)\bigg)$. For which value of $i$ is $p_i$ the largest? (A) 3 (B)...
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### Properties of the diff of a sorted uniformly generated set

I am studying a set of uniformly generated points, more concretely the distance between the points. When the set is unsorted the histrogram shows it is normally distributed and that matches my ...
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### Sensitivity analysis with a uniform distribution

Is it possible to perform a sensitivity analysis on a uniform distribution? For more explanation: I can perform a sensitivity analysis on an exponential distribution by systematically varying the ...
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### Conditional Probability Uniform Bivariate Transformation Distribution

I'm reviewing probability theory from years ago and am a bit rusty. I'm not sure how to calculate the conditional probability for a uniform distribution after a bivariate transformation. Suppose X and ...
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### Convergence in Probability (Analytical Solution Verification)

Problem: Let $X_1,X_2,\cdots$ be independent random variables that are uniformly distributed over $[-1,1]$. Show that the sequence $Y_1,Y_2,\cdots$ converges in probability to some limit, and identify ...
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### Maximum likelihood estimator of $\theta$ for uniform distribution [closed]

I know that , For Uniformly Distributed random variables $X_1,X_2,\dots,X_n$ $\in \mathcal{R}$, the p.d.f is given by: $f(x_i) = 1/θ$ ; if $0≤x_i≤θ$ $f(x) = 0$ ; otherwise If the uniformly distributed ...
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### Question on a statistics symbol used in describing uniform distribution / likelihood function [duplicate]

When the function of a sample from a uniform distribution is described, there seems to be a symbol (either 1 or I) next to 1/theta. For example, the likelihood function of a sample from a uniform ...
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### finding PDF of Y, given Y|X [closed]

$$Y|X\sim Bin(X,n)$$ $$X\sim U([0,1])$$ How can I find the PDF of Y? I know that: $$\Bbb P(Y=k)=E_X[\Bbb P(Y=k)|X]$$
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### Confidence interval for simple sample, uniform distribution [duplicate]

Let $X_1, X_2$ be a simple sample from uniform distribution $U[0, \theta], \theta > 0$. Find constant $C$ such that an interval $(CX_{2:2}<\theta<\frac{1}{\sqrt\alpha}X_{2:2})$ is a ...
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### If V=X+Y how to prove that there is no independent random variables X,Y make V a uniform distribution [duplicate]

If V=X+Y,how to prove that there is no independent random variables X,Y (with the same distribution function) make V a uniform distribution function on [0,1]
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### Density of square root of sum of squared independent uniform random variables [duplicate]

Let $X \sim U(-1, 1)$ and $X \sim U(-1,1)$. We want to find density function of $W = \sqrt{X^2 + Y^2}$. I got stuck and I have no idea, where I am making a mistake. This is my approach. Let $F$ be a ...
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### Determine if clusters of combined values are coincidental

I have a set of measurement results like this (hex numbers): 30AF, 31AE, 30AF, 30AE, 31AE which vary only slightly, there are usually 3-4 distinct values per measurement set of 30 results(could ...
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### Uniform distribution, estimates, MVUEs and Cramer Rao Lower Bound

As a revision exercise, I'm going through all of the distributions and deriving estimators. I've gotten to the $Uniform$. I've worked out the MLE and MOM estimators. The next step is to consider ...
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### Relationship between two randomly-generated variables

Using stata, I generate two random variables and regress them with each other. ...
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### how to write the joint density of two correlated uniform random variables?

Suppose the marginal distributions of $X$ and $Y$ are both $U[a,b]$, where $U[a,b]$ denotes uniform distribution on $[a,b]$. When $X$ and $Y$ are correlated, how to write their joint density for some ...
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### Why does Uniform distribution make sense?

This might be a dumb question, but I am suddenly confused on how to understand the PDF of a uniform distribution. For instance, the PDF of standard uniform is always equal to 1... How is that ...
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### generating a uniform random variable from the first digit of an exponential random variable?

in "introduction to probability models", Ross talks about simulating with the rejection method, and he needs an exponential random variable, and a uniform random variable (used only for checking ...
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### Independence for subsets of [0,1]

I'm struggling with this problem: Let $\mathbb{P}$ be the uniform measure on $[0,1].$ Define $A=(a,b)$ and $B=(c,d)$ with $a<c.$ State the necessary and sufficient conditions for $A$ and $B$ to be ...
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### Connection between uniform distribution on a set and uniform sampling from a set - intuitive pictures and necessary mathematical formulas

What's the connection between uniform distribution and uniform sampling from a set $S$? Are these two terms synonymous: "uniform sampling from a set" and "sampling from a set according to a uniform ...
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### Ratio of Two Uniform Random Variables [duplicate]

If X1 X2 are independent Uniform variates on (0,1), Find the distribution of Z=X1/X2. I tried using the CDF method where P(X1<=zX2) is equal to z/2 when z is in(0,1). However, I am unable to find ...
I have a problem with the scale uniform interval estimator (Example 9.1.6, page 419, Casella-Berger). Let $X_1,\dots,X_n \sim \text{IID U}(0,\theta)$ be our observed data. We are interested in an ...