# Tagged Questions

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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### Mean distance of random points on a rectangular grid

I have a $N\times N$ grid of side $L$. Each gridpoint can be black or white and a ratio $r$ of the points is black. I want to predict the mean distance between two black points. The most appropriate ...
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### Joint density of Triangular RV and Maximum of Triangular RVs, parameterised by Uniform RV

Let $x$ be drawn from the uniform distribution on $[0,1]$. $x$ parameterises the Triangular distribution $Y$ with support $[0,1]$. I.e.,  f_Y(y_i | X = x) = \begin{cases} \frac{2y_i}{x} \quad \...
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### Uniform distribution density function

Let's say we have two random variables $T_1$ and $T_2$ and the joint density function of the two is uniform over the region $0\leq t_1\leq t_2 \leq L$, where L is a positive constant. Then the area of ...
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### Distribution of function of uniformly random variables

I am sorry if there is no simple answer to this or the answer is completely obvious but I am approaching my wits end here. Probability isn't my forte, nor am I even a mathematician. I am essentially ...
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### Partition Theorem to show $P(W \gt Z)$

I am confused as to how to use the partition theorem on the following example? Any help is appreciated! Suppose that W has a U(0,1) distribution and suppose that W is independent of the random ...
### Prove that uniform distribution on a set of vertices $V$ is stationary if the graph is regular.
I was going through Random walks on graphs: A survey It was stated that: Uniform distribution on a set of vertices $V$ is stationary if the graph is regular. Can anyone give me some hints to ...
Let $(X_1,X_2,\ldots,X_n)$ be a random sample from uniform distribution on interval $(\theta_1, \theta_2)$. Find a uniformly most powerful unbiased test of size $\alpha$ for testing \$H_0: \theta_1 &...