# 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.

1,350 questions
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### Picking points on a sphere at random

Suppose we pick up $N$ points uniformly at random on a sphere. The probability that these points lie within a 'fixed' hemisphere is easily calculated to be $1/2^N$. But what is the probability that ...
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### Probability the three points on a circle will be on the same semi-circle

Three points are chosen at random on a circle. What is the probability that they are on the same semi circle? If I have two portions $x$ and $y$, then $x+y= \pi r$...if the projected angles are $c_1$ ...
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### Not getting the answer as given in Feller

Find the probability that the equation $x^2-2ax+b=0$ has complex roots, if $a,b$ are random variables following the Uniform $(0,h)$ distribution individually and independently. So we effectively need ...
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### Average sine of an angle between two rays in a cone

I'm looking for an average value of sine of an angle between two rays, lying within a cone with a certain angle. Given a cone with an aperture of ${2\chi}$ and two rays lying within the cone. The ...
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### Distribution of minimum of difference between uniforms $(0,1)$

Let $U_1,...,U_N$ be a sequence of independent uniformly $(0,1)$ random variables. Define $Y_k := U_k - U_{k+1}$. Find the distribution of $\min\left\{Y_k\right\}_{k=1}^{N-1}$. I've get the ...
Where $\frac{1}{\infty}$ and $\frac{\infty}{\infty}$ are both undefined terms that generally lead to nonsense, I'm wondering if we can assert that...: $$\frac{1+1+1+\cdots}{1+1+1+\cdots} = 1$$ ...or ...