# Questions tagged [uniform]

The uniform distribution describes a random variable that is equally likely to take any value in its sample space.

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### Circular Uniform Distribution Function Question [closed]

I have a question related to the cdf portion of the problem below: Problem. Suppose $W$ is uniformly distributed on $[0, 2\pi)$, and let $Z = (X, Y) = (\cos(W), \sin(W))$. What are the marginal ...
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### test if one event is more frequent than another

I am observing 2 types of events with counts (A and B) and I want to know if one is more frequent than the other for the time that I am observing. I know the chance of an appearance is uniform over ...
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### Continuous distributions function has uniform distribution [closed]

Let X be a random variable with continuous distribution function F (x) than it has uniform distribution ,i.e.,U (0,1). Please prove this theorem.
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### Pdf of the sum of two independent Uniform R.V., but not identical

Question. Suppose $X \sim U([1,3])$ and $Y \sim U([1,2] \cup [4,5])$ are two independent random variables (but obviously not identically distributed). Find the pdf of $X + Y$. So far. I'm familiar ...
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### Sobol variance based decomposition

I have 6 input variables, each of which is normally distributed. Can I use Sobol variance-based sensitivity analysis? I have read some articles where they said that input variables must have uniform ...
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### Creating our own normal distribution function in R [closed]

I have a homework question which requires me to create my own standard normal distribution function which I had derived. Nonetheless, I have problem doing so. What I did was to have two independent ...
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### Algorithm for uniform sampling with bounded replacement

Is there a simple algorithm to sample from the uniform distribution on sequences of $n$ numbers, each taking one of $m$ integer values from $0$ to $m-1$, where each value can be repeated at most $r$ ...
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### Why does the distribution of the exponential random variable change to uniform distribution in this case?

I came across this very interesting question in a forum: If both X and Y are independent and exponentially distributed with parameter $\lambda$, find $E[X^2|X+Y]$ Someone gave the solution and ...
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### Why do we need to triangulate a convex polygon in order to sample uniformly from it?

Suppose I want to uniformly sample points inside a convex polygon. One of the most common approaches described here and on the internet in general consists in triangulation of the polygon and generate ...
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### Is there an explanation for why there are so many natural phenomena that follow normal distribution?

I think this is a fascinating topic and I do not fully understand it. What law of physics makes so that so many natural phenomena have normal distribution? It would seem more intuitive that they would ...
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### A question about a sum of squares of uniform random variables

For independent and identical $V_1,V_2\in U(-1,1)$, what is the probability that $V_1^2+V_2^2<1$? I tried but can't get an answer, the answer is $\frac{\pi}{4}$
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### Maximum Likelihood Estimator of $\theta$ [closed]

Let $X_i$ be i.i.d $U(-\theta,2\theta)$ for i=1,2,...n. $f(x)=\frac{1}{3\theta}$ and $L(\theta)=(3\theta)^{-n}\mathbb{1}_{[-\theta<X_{(1)}<X_{(2)}<...<X_{(n)}<2\theta]}$. I don't know ...
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### Generating uniform points inside an $m$-dimensional ball

The present question follows on from some other questions on this site asking how to generate uniform points on a disc (see e.g., here, here and here). The natural extension of that problem is to ...
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### How to measure whether a discrete distribution is uniform or not?

Say I have two vectors [1,2,1,2,2] and [1,2,1,1,1]. The number at each dimension is the frequency of one element. How do I measure whether these two vectors are close to the uniform distribution? I ...
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### When should I use the Normal distribution or the Uniform distribution when using Xavier initialization?

Xavier initialization seems to be used quite widely now to initialize connection weights in neural networks, especially deep ones (see What are good initial weights in a neural network?). The ...
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### continuos uniform distribution pdf value at upper bound

What is the most formal (and coerent with probability theory) definition for the value of pdf(b) where b is the upper bound of the support of the continuos uniform distribution U(a,b) ? We can choice: ...
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### Why does deviation from uniform distribution suggest skewed-t model may not provide adequate fits for copula model

I read a book titled "Statistics and Data Analysis for Financial Engineering with R examples". At page 203, I read the following paragraph. "Figure 8....
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