# 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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### Find the a posteriori probability? (Ch-4,Exercise-21, Probability, Random Variables and Stochastic Processes-Papoulis)

The probability of heads of a random coin is a random variable p uniform in the interval (0, 1). (a) Find P{O.3 <= P <= O.7}. (b) The coin is tossed 10 times and heads shows 6 times. Find the a ...
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### Is $3-4U$ equivalent to $4(1-U)$?

If $U$ is defined to be the uniform distribution on $(0,1)$, is it true that $3-4U\sim4(1-U)$?
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### Expected number of regions with $n$ random lines in a circle

There are $n$ random lines drawn in a circle, defined by endpoints being uniform on circle. I am trying to figure out the expected number of regions separated by $n$ lines. I know $f(0)=1$, $f(1)=2$ ...
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### The density function of the sum of n independent uniformly distributed random variable on $(-1,1)$ is supported on $[-n,n]$

This question arose from the statement after Exercise 3.3.6 of Durrett's probability. Exercise 3.3.6: Show that if $X_{1}, \cdots, X_{n}$ are independent uniformly distributed on $(-1,1)$, then for ...
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### Universality of the uniform in the context of the Rayleigh distribution

I am currently exploring a theorem called universality of the uniform: Let $F$ be a CDF which is a continuous function and strictly increasing on the support of the distribution. This ensures that ...
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### Let $X$ be an r.v. with CDF $F$. Then $F(X) \sim \text{Unif}(0,1)$?

I recently encountered a theorem called universality of the uniform: Let $F$ be a CDF which is a continuous function and strictly increasing on the support of the distribution. This ensures that ...
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### Uniform distributions: location-scale transformation

My textbook, Introduction to Probability, first edition, by Blitzstein and Hwang, says the following: In a location-scale transformation, starting with $X \sim \text{Unif}(a, b)$ and transforming ...
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### Showing independence of ratio of ordered statistics for uniform distribution

From An Intermediate Course in Probability by Allan Gut Suppose that $X\in U(0,1)$. Let $X_{(1)},X_{(2)},\ldots,X_{(n)}$ be the order variables corresponding to a sample of $n$ independent ...
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### Let $U_1,U_2,…$ be a sequence of independent uniform $(0, 1)$random variables, question about $\Pr(N > n)$

Let $U_1,U_2,...$ be a sequence of independent uniform $(0, 1)$random variables and let $$N:=\min\{n\geq 2: U_n>U_{n-1}\}$$ $$M:=\min\{n\geq 2: U_{1}+\cdots+U_n>1\}$$ Show that ...
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### Twist on classic interview question. $P(X > 3Y)$ where $X,Y$ are uniform random variables

So there's this very classic probability question that says: Given$X, Y$ two INDEPENDENT uniform random variables in $[-1,1]$, what is $P(X > 3Y)$? Of course, there are alterations where the ...
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### How do you compute uniform distribution with only mean and proportion given?

Machine A produces mints that have a label weight of 50g and is believed the weights of the weight is uniformly distributed, with a mean of 51.5g and 70% of them less than 52.5g. What's the ...
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### Sort a set of arrays such that the mean-member delta of each array position is minimized

Given n number of arrays A in the format An = [xn, yn, zn] where X, Y, and Z are collections in the format X = [x1, x2, x3, ...xn], Y = [y1, y2, y3, ... yn], and Z = [z1, z2, z3, ...zn], create a ...
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### Unbiased estimator for UNIF($-\theta, \theta$)

I am searching for an unbiased estimator for $\theta$ in a UNIF($-\theta, \theta$) distribution, which looks like $\hat\theta = c(X_{n:n} - X_{1:n}$). The question is to search for the c that makes ...
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### Figuring Out Marginal Density by Looking at Plot of Joint Density

I have the below plot of the joint density of X and Y. X and Y are continuous random variables. X takes on values between 0 and 2 while Y takes on values between 0 and 1. Can someone please explain ...
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### Euclidean distance of two uniform random variables

Two random variables $X$ and $Y$ are uniformly distributed, the pdfs of which are given by $f_{X}\left(x\right) = f_{Y}\left(y\right) = 1/r$. I am trying to obtain $Z = \sqrt{X^2 + Y^2}$. I tried the ...
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### Joint probability density for non-identical Uniform random variables

Let $~X,~ Y~$ be uniform on $~[0, 3] × [2, 4]~$. Find $~P(X + Y ≤ 5)~$ and $~X~$ and $~Y~$ are independent. My approach: Using convolution formula. Difficulty I am facing: Understanding the limits ...
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