# Questions tagged [uniform-distribution]

For questions involving random variables uniformly distributed on a subset of a measure space. To be used with [probability] or [probability-theory] tag.

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### How to find the pdf of the minimum of absolute differences of Uniform distributions.

Let $X_1$,$X_2$ and $X_3$ are independent random variables that are uniformly distributed over $(0;b), b>0$. What is the probability density function of z=min($Y_1$,$Y_2)$, where $Y_1=|X_1-X_2|$ ...
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### Uniform distribution- independent random variable max and min

Let $X,Y \sim U_{[-1,1]}$ are independent random variables. Let us define $U=\max (X,Y)$ and $V=\min(X,Y)$. Are random variables $U,V$ independent ?
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### joint/marginal pdfs over parallelogram integration limits

I am TERRIBLE at figuring out the limits of integration when finding PDFs. Say $a, b$ are uniformly distributed over the parallelogram with vertices $(0, 0), (1, 0), (2, 1), (1, 1)$. Find the joint ...
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### Random Area and Perimeter

Lt A and L denote the area and perimeter of a rectangle with length $X$ and height $Y$, such that $X$ and $Y$ are independent, and uniformly distributed on $(0,1)$. Find the density function of $A$ ...
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### Create random variable Expo from Unif(0,1)

Working through some problems from Introduction to Probability (Blitzstein) Let U~Unif(0,1). Using U, construct X~Expo($\lambda$). My work: (edited with updates on CDF and inverse function) PDF ...
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### Optimal number of experiments

There is a random variable and we know that it is either uniformly distributed on $(0, 1)$ or uniformly distributed on $(0, \frac{1}{2})$. Both cases are equally likely to be. We are to guess the ...
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### Find the probability that the roots of the quadratic $U_1x^2+U_2x+U_3$ are real

The question, from the textbook: Mathematical Statistics and Data Analysis Let $U_1, U_2, U_3$ be independent random variables uniform on $[0,1]$. Find the probability that the roots of the quadratic ...
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### Probability that Carl has to wait at least 10 minutes for one of the others and for both of the others to show up?

This question is for the other subquestions for the same problem here. For those not willing to click the link, I will post the exercise problem here as well. Alice, Bob, and Carl arrange to meet ...
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### Symmetry of Uniform Distribution PDF

I'm studying probability theory and came across an exercise problem that I couldn't quite understand, even with the solution, and was hoping someone could give me some insight. Alice, Bob, and Carl ...
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### PDF of Z = XY for Jointly Uniform (X,Y) with Parabolic Region

"Suppose that $(X,Y)$ is uniformly distributed on the subset of $\; \mathbb R^2$ defined by the inequalities $0 < X < 1$ and $0 < Y < X^2$. Determine the probability density function of ...
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### Sum of squares of uniformly distributed variables

Let X, from which I draw N samples, have a uniform distribution on $(-1,1)$. What is the distribution of the sum of squares -- $\sum\limits_{i=0}^{N-1} {x_i}^2$ -- and its variance? We can assume N to ...
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### What is the distribution of a finite sum of products of i.i.d uniformly distributed variables and their indicators

Well , the case is : let $X_i$ ~ $U[0,X_{max}]$ , $i=1,...,N$ - i.i.d random variables from a single uniform distribution. Let $I${$X_i>C$} be an indicator function of $X_i$ ($C \le X_{max}$). So , ...
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### Distribution of max and min

If $X_1,X_2,\ldots,X_n,\ldots$ are iid uniform random variables on $[-1,1]$. What's the distribution of $X_{\max,n} = \max_{1 \leq i \leq n} X_i$ and $X_{\min,n} = \min_{1 \leq i \leq n} X_i$? My ...
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### Conditional probability with uniform distributions: A company will experience a loss X that is uniformly distributed between 0 and 1

I'm trying to solve the problem: "A company will experience a loss X that is uniformly distributed between 0 and 1. The company pays a bonus to its employees that is uniformly distributed on the ...
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### Strongly consistent estimator for uniform distribution on $[-\theta, \theta]$

Let $X$ be a random variable having uniform distribution on the segment $[-\theta, \theta]$. I construct the following estimator for unknown parameter $\theta$.  \hat{\theta}(x_1,\ldots,x_n) = \frac{...
$X_1 \sim \mathrm{Unif}(0,1)$ if $X_1=x_1$, $X_2 \sim \mathrm{Unif}(x_1,x_1+1)$ if $X_2=x_2$, $X_3 \sim \mathrm{Unif}(x_2,x_2+1)$ for $n \geq4$, $X_n$ is defined the same way. How do I calculate \$E(...