# 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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### Uniform distribution with Gaussian Priors

Let's say i've got a uniform distribution defined as follows $$X \sim U[\min (\theta_1,\theta_2),\max (\theta_1,\theta_2)]$$ I've also got that $\theta_1,\theta_2$ are i.i.d zero-mean normal ...
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### If A is distributed uniformly on [8,10] and B on [9,11], what is the probability that B<A?

I was asked this question in an interview, and did not initially answer correctly though I still think my interpretation may have been the correct one. The question was: There are two delivery ...
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### Convolution for uniform distribution and standard normal distribution

Consider a random variable $U$ that has a uniform distribution on $(0,1)$ and a random variable $X$ that has a standard normal distribution. Assume that $U$ and $X$ are independent. Determine an ...
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### Why is the sum of probabilities in a continuous uniform distribution not infinity?

The probability density function of a uniform distribution (continuous) is shown above. The area under the curve is 1 - which makes sense since the sum of all the probabilities in a probability ...
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### $X_i \sim \text{Uniform}(0, \theta)$ iid; $Y = \max{(X_1,..,X_n)}$. Why is $\theta$ necessarily larger than $y$?

I'm going through Statistical Inference by Casella & Berger, and on page 419, in the intro section of interval estimation there is the following example (note: most of the text was left out as it'...
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### General rule uniform distributed classes

Given a classifier working with double values e.g. between 0 and 1. There are two classes with different ranges. Their distributions are uniform, however, one class is more likely. Is picking always ...
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### Finding maximum likelihood estimator, symmetric uniform distribution

Let $X_1, ...X_n$ be IID random variables with uniform$[ -\theta , \theta ]$ . I need to find the Maximum Likelihood estimator (MLE) of $\theta$. My work is as follows, The likelihood function is , ...
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### calculating correlation between binary vectors with generating with uniform distribution

I am working with some correlated binary files. I want to know, what is your opinion for calculating the correlation between binary vectors? for example, if I have two binary vectors X1 and X2 ...
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### The probability of photon collision

I was reading a textbook and I couldn't figure out something that seemed really obvious: Assume that the space is uniformly and randomly filled with stars, and the mean radial distance between the ...
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### What is the ratio of a N[0,1] and U[-1/2,1/2]?

I have come across a problem where I can reasonably assume that the numerator is a uniform distribution of the type U[-a,a], i.e., centered on zero, and the denominator is N[0,b]. This seems to be ...
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### how to calculate the standard deviation of the sum of multiple uniform distribution

Given several independent uniform distributions, such as runif(0,5) and runif(0,50), how to calculate the sd of the sum of the two functions? And in what scenario would one needs to consider the sum ...
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### How to determine if individual is related to a given population

I would appriciate your help in the following problem: I've been told that the bonobos height is uniformly distributed, with a,b equal to [70,76] respectivly. In this group, one individual (height=70....
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### Sufficient statistics for Uniform $(-\theta,\theta)$

So, I know that $\max(-X_{(1)},X_{(n)})$ is a sufficient statistic for the parameter $\theta$. But can I also say that $(X_{(1)},X_{(n)})$ are jointly sufficient for the parameter $\theta$ ? In other ...
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### The Distribution of max(X,1/X)

If $X \sim \text{U}(0,1)$, what is the distribution of $Y = \max(X,1/X)$? I know for this particular problem, $Y = \max(X,1/X) = 1/X$, whose distribution can be easily attained directly. However, I've ...
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### PDF of the maximum likelihood estimator of a uniform distribution

Suppose $\{X_1, \dots , X_n \}$ is a random sample from: $$f_X(x; \theta) = \frac{1}{\theta} \text{, for } 0 \leq x \leq \theta$$ The Likelihood function is easy to calculate:  L_Y(\theta; y)...
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### guessing a 4-digit access code

The company I work for shares a building with another company, so when we need to access that building, we use a 4-digit access code (which never changed in several years) for the main door, and then ...
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### Distribution of extreme values, case of uniform

Question: For $U_1 , \dots, U_n$ i.i.d. $U \sim \mathrm{unif}[0,1]$, we want to find the asymptotic distribution of $Z_n = n(1-U_{(n)})$ where $U_{(n)} = \max(U_1 , ... , U_n)$ I found this: ...
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### Is there a continuous version of the Uniform distribution?

The Uniform distribution is not differentiable. Is there a differentiable distribution that approximates a Uniform?
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### CDF of Z=XY with X~Uniform(0.5,1.5) and Y~Uniform(0.8,1.5)

I am looking for the CDF of the product of two independent random variables (X and Y) with uniform distributions. Both random variables uniform distributions have interval boundaries (upper and lower ...