# 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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### Show that $P(N \geq n) = (1-e^{-\lambda})^n/ \lambda^n$

The lifetime $X$ (in days) of a device has an exponential distribution with parameter $\lambda.$ Moreover, the fraction of time which the device is used each day has a uniform distribution over the ...
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### “Fragmentation” of a distribution (from paper)

I've been reading a paper by Robert Morris ("Sets, Scales and Rhythmic Cycles; A Classification of Talas in Indian Music") and came across a formula that I've found a bit tricky. He is referring to ...
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### Targetting the distribution of distances between points

For a certain problem, I need to make distance dependent statistics, but with the constraint that the number of sampling points, $N$, should be kept as small as possible. To be more specific I need to ...
Let $(X_n)_n$, $n = 1, 2, \dots$, be an iid sequence of random variables uniformly distributed on $(0, 1]$. Set $S_0 = 1$ a.s. and, for $n = 1, 2, \dots$, set $S_n = \prod_{k=1}^n X_k$. Compare $S_n$ ...
Let $U_{t}$ be iid Uniformly distributed on (0,1). Suppose $\hat{\theta}_{T}\stackrel{d}\rightarrow \theta^{*}$ with $\theta^{*}$ some random variable on (0,1). I believe \$\sum_{t=1}^{T}I(U_{t}\leq \...