# 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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### What is the benefit of using permutation tests?

When testing some null versus alternative hypotheses by a test statistic $U(X)$, where $X = \{ x_i, ..., x_n\}$, apply the permutation test with the set $G$ of permutations on $X$ and we have a new ...
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### Getting variance of function of two uniform RVs [duplicate]

Have two independent RV's $X$ and $Y$ sampled uniformly from $[0,1]$ and $C = (X-Y)^2$. Want $V(C$). Rewrote as $V((X-Y)^2) = V(X^2) - 4V(X)V(Y) + V(Y^2)$ but that's too messy. Is it correct to write ...
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### Why is the mean of the natural log of a uniform distribution (between 0 and 1) different from the natural log of 0.5?

For a uniformly distributed variable between 0 and 1 generated using rand(1,10000) this returns 10,000 random numbers between 0 and 1. If you take the mean, it ...
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### Example: Writing the joint PDF $f(x, y)$ as the product of a marginal and a conditional probability function

I am presented with the following notes on Bivariate distribtions: If we can write the joint probability density function $f(x, y)$ of a pair of random variables $(X, Y)$ as the product of a marginal ...
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### Maximum likelihood estimator in Uniform distribution [closed]

For Random sample with uniform distribution in Tetha< x< Tetha +1 What's the maximum likelihood function how can we maximize it?
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### Estimating parameters for the product of a lognormal random variable and a uniform r.v

Suppose I have a random variable which I suspect is the product of a lognormally distributed random variable $X$ and an independent uniformly distributed variable $U(0, 1)$. (The variables are the ...
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### Log-uniform distributions

I am having some difficulty understanding what log uniform distributions are. Suppose that $\log X$ is uniformly distributed on the interval $[1,e]$. How do I describe $P(X=x)$? It seems like there ...
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### Uniform distribution inside Log

What is the meaning of putting uniform distribution inside log? See page 5 of this paper (Corentlin et al.) To make it more clearer, within my knowledge, I think I should put a single value inside ...
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### A data-independant transformation to discretize a range of values non-uniformly

I am sure this is trivial, but I am looking for a transformation that nonuniformly discretizes all values of a range into several bins. The bins should be variant and I'd like them to be smaller ...
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### Variance of Estimator (uniform distribution)

In my script for statistical signals, I have some troubles to get the same result for the variance of an estimator $T$. Here is the example: Given the observations $X_1, \dots , X_N$ of a uniquely ...
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### How to generate a uniform random variable from [1,7] if given a uniform[1,5] RV generator? [duplicate]

I saw this as a question on glassdoor and I've seen similar questions elsewhere. Can someone explain the intuition of how to solve a problem like this? There are two scenarios The uniform RVs in ...
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### Is there a plateau-shaped distribution?

I am looking for a distribution where the probability density decreases quickly after some point away from the mean, or in my own words a "plateau-shaped distribution". Something in between the ...
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### Survival in two period game: mean of z|z<v with z=xy, x~U(a,b) and y~U(c,d)

I am looking for the functional form to describe the following: A random shock $x\sim Uniform(a,b)$ is multiplied with a second shock $y\sim Uniform(c,d)$. What is the mean value of all combined ...
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### Spearman $\rho$ as a function of Pearson $r$

It is common to talk about the linear correlation, Pearson's $r$, between two random variables $\{(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)\}$ as having two components: a) the copula and b) the marginal ...
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### Reference books on uniform spherical distributions in multiple dimensions [duplicate]

QUESTION What is a citation of a book whose scope includes the uniform distribution [1] that is generalized to an $n$-ball [2]? Among other things, I'd like to read a book that include such ...
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### Calculating the sum of dependent uniform random variables

My question derives from Problem calculating joint and marginal distribution of two uniform distributions. So, suppose we have random variables $X_1$ distributed as $U[0,1]$ and $X_2$ distributed as ...
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### What is the probabilty that X > 2 conditioning on Y = 2? (Homework)

another homework question here. Let š be a binomial random variable with 10 number of trials and 0.2 probability of success. Let X be a uniformly distributed random variable over the interval [0, 3]. ...
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### How many classmates does a freshman have?

The freshmen at East China Normal University has just received their student ID. Let the last three digits of a student ID be ABC, then A is the class he is in, whereas BC is his number in the class. ...
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### Transforming a uniform random variate to points on a circle

Sample $U \sim \text{Uniform}(0,\sqrt{2}-1)$. Accept $U$ with probability $1/(1+U^2)$ (else reject and sample again). Set $X = 2U/(1+U^2)$ and $Y = 1-UX = (1-U^2)/(1+U^2)$. With probability 1/2, ...
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### How can I generate 2 sets of variables from different distributions with a correlation between them in r? [duplicate]

I am working in R and would like to generate 40 numbers from $\mathrm{N}(0,1)$ and another 40 from $\mathrm{Uniform}(0,2)$ with a negative correlation (for example: $r = -0.45$) between them. The ...
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### Draw integers independently & uniformly at random from 1 to $N$ using fair d6?

I wish to draw integers from 1 to some specific $N$ by rolling some number of fair six-sided dice (d6). A good answer will explain why its method produces uniform and independent integers. As an ...
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### The joint pdf of sample maximum and sample mean for uniform distribution?

Assume $$\{X_i\}\stackrel{\mathrm{i.i.d.}}{\sim} \mathcal{Uniform}(0,1)$$ Find the joint p.d.f. of $$X_{(n)} \hat= \max \{X_1,X_2,\ldots,X_5\}\quad\text{ and }\quad \bar X\hat=\sum^n_{i=1}{X_i}$$ ...
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### Histogram bin size to show deviation from uniform distribution [duplicate]

Simple question: Is there a rule of thumb for number of bins in a histogram with a uniform distribution? Details: I have a stochastic computer simulation that produces, as a test, $n$ values that ...