# 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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### For the case of Pokemon IV, what distribution is it for the percentage value?

I took statistics some 25 years ago, and remember that if students take a test, then the test scores actually form a bell curve. But somebody claimed that for Pokemon IV: a random number from 0 to 15 ...
826 views

### Normal Distribution with Uniform Mean

I'm trying to understand the distribution, mean, and variance of a normal random variable, with the mean parameter having a uniform distribution. Based on my R simulations it seems that this compound ...
904 views

### Finding UMPT for uniform distribution with varying support

$\textbf{Problem}$ Let $X_1,\dots,X_n$ be a random sample from $f(x;\theta) = 1 / \theta$, where $0 < x < \theta$. We want to test $H_0: \theta \leq \theta_0$ versus $H_1: \theta > \theta_0$. ...
705 views

### Generate random numbers from “sloped uniform distribution” from mathematical theory

For some purpose, I need to generate random numbers (data) from "sloped uniform" distribution. The "slope" of this distribution may vary in some reasonable interval, and then my distribution should ...
413 views

453 views

### Bayes Rule Uniform Distribution

For Bayes rule, if my likelihood, and prior distribution are both uniform, is my posterior distribution also guaranteed to be uniform? In addition to this, if I apply some transformation to a ...
143 views

### Easier way to find $\mathbb{E}\left[X_{(2)}| X_{(1)}, X_{(3)}\right]$?

Consider 3 iid samples drawn from the uniform distribution $u(\theta, 2\theta)$, where $\theta$ is parameter. I want to find $$\mathbb{E}\left[X_{(2)}| X_{(1)}, X_{(3)}\right]$$ where $X_{(i)}$ ...
49 views

### Is it possible, practically, to sample any point on 0 to 1 under Uniform sampling?

I am solving optimization problems where I am trying to find the minimum of a function over some sample space $\mathcal{X}$, i.e., $\min\,f(x):x\in\mathcal{X}$. Now the optimization algorithm I am ...
2k views

### 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 ...
365 views

### Given $X,Y\sim i.i.U[0,1]$, what is $P(X<Y)$?

Let a, b be real numbers randomly selected independently and uniformly from the range of (0,1). What is P(a < b)? The problem here is that a can be equal to b, so is P(a < b) ≈ 0.5 or P(a ...
540 views

### Standard deviation of the sum of a discrete uniform

If I randomly generate a number between 1 and 10.... 10 times, and then total all the numbers, what will the standard deviation of that total be? I'm pretty sure the mean of the total will be 55.5, ...
93 views

### Expected root of quadratic random polynomial

Suppose $A,B,C$ are i.i.d. random variables with uniform distribution on $[-1,1]$. I'm interested in the expected roots of the polynomial $Ax^2 + Bx + C$, which are complex random variables given by ...
346 views

### Improving Chebyshev-type bound for discrete uniform distribution

I take $N$ samples from a fully specified, discrete, finite uniform random variable $X$ with mean $\mu$ and variance $\sigma_X^2$. I want to find the probability that the absolute error of the ...
### How to efficiently choose $n$ subset out of a set of $m$ many numbers, in a randomized uniform manner?
Problems: It is fairly simple: we have a list of numbers $x_1, x_2, \ldots,x_n,\ldots, x_m$. Our goal is to randomly and uniformly choose a subset of $n$ many numbers out of these. This means that, ...
I've got 2 independent draws from these two distributions :$X\sim U(0,1)$ and $Y\sim U(0,2)$. I want to find $E(\max(X_,Y))$. I know that for two (0,1) independent Uniforms: \$P(\max(X,Y)<z)=P(...