# 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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### Expectation of the largest order statistic from uniform random variables

If $X_1, ..., X_n$ are iid random variables from the Uniform[$0,\theta$] distribution, where $\theta >0$, compute the expectation of the largest order statistic denoted $X_{(n)}$. I am looking to ...
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### Ambulance problem with joint random variable

An ambulance travels back and forth, at a constant speed, along a road of length $L$. At a certain moment of time an accident occurs at a point uniformly distributed on the road. [That is, its ...
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### Explicit calculation of the arccos-1-kernel

I have given the following problem from the draft book of Francis Bach: "For $(w,b/R)$ uniform on the sphere and for the ReLU activation, compute the associated kernel as a function of the cosine ...
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### Laplace's Rule of Succession and Bessel's Correction

Are applying Laplace's Rule of Succession to estimate a probability distribution from samples and applying Bessel's Correction (in reverse, perhaps) to estimate population statistics from sample ...
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• 703
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### what is the variance of difference between max and min of n i.i.d uniform variables : U(0,1)

It is an interview question: calculate the variance of difference between max and min $$variance[\max(\{X_i\}) - \min(\{X_i\})].$$ Here $\{X_i\}$ is n i.i.d uniform variables : U(0,1). I know it is ...
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### Estimate: $\pi \to e \to \log(2) \to G$ by sampling uniform distribution

Successively: $\pi \to e \to \log(2) \to G$ were calculated/estimated by sampling uniform distributions. Method: With a normal distribution $\pi$ can be calculated with help of the PDF (probability ...
1 vote
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currently I'm stuck with some probability task (I will provide my solution below): We have interval of 10 minutes (in other words [0; 10]). Two people ("A" and "B") come after each ...
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### Uniform distribution over order simplex

Consider the set of all vectors $x \in [0,1]^K$ that are monotone, i.e. $0\leq x_1\leq x_2\leq ... \leq x_K\leq 1$. This set is known as orthoscheme or order simplex. Is there a formula for the ...