# Tagged Questions

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

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### Why would predicted values be normally-distributed when the actual values are uniform?

I'm building a supervised learning model where the target variable is a uniformly-distributed continuous value ranging from 0-1 (originally a rank value from 1-38000, then scaled down to 0-1). The 20 ...
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### Probability of a random variable to be the largest among others

Let us have $N$ random variables generated by uniform distribution. That is, $$u_i \sim \mathcal{U}(0,1),\quad i=1,\ldots,N$$. What is the probability of $u_N$ being the largest? I.e., how can I ...
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### Random Balls in Random Buckets: What are the characteristics of the distribution?

I have N buckets, numbered 1 to N. I draw k random integers, uniformly distributed in the range 1 to N, with replacement, and for each integer I drop a ball into the corresponding bucket. k can be ...
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I have two uniforms distributions, $X_1 \sim\it{U}(a,b)$ and $X_2\sim\it{U}(X_1+\delta,b+\delta)$. I would like to compute $P(X_2\in[a+\delta,b+\delta])$. So I do this: $$\begin{eqnarray*} ... 3answers 1k views ### Consider the sum of n uniform distributions on [0,1], or Z_n. Why does the cusp in the PDF of Z_n disappear for n \geq 3? I've been wondering about this one for a while; I find it a little weird how abruptly it happens. Basically, why do we need just three uniforms for Z_n to smooth out like it does? And why does the ... 0answers 23 views ### Sample/Filter nonuniformly distributed values so that result follows a uniform distribution I have a dataset with a nonuniform distribution. I want to sample it so that the result is uniformly distributed. If I know the class of the example, with what probability should I choose it to get a ... 5answers 1k views ### Fake uniform random numbers: More evenly distributed than true uniform data I'm looking for a way to generate random numbers that appear to be uniform distributed -- and every test will show them to be uniform -- except that they are more evenly distributed than true uniform ... 1answer 123 views ### Probability model question [closed] Counts of the number of broken bones in college athletes during the season would be best represented by which of the following probability models? Question options: Binomial --Thinking this is the ... 1answer 85 views ### Weak Convergence Here is the problem (not homework), Let U_1,\cdots,U_n be i.i.d. uniform(-n,n) random variables. For -n<a<b<n, we set 1_{U_i}(a,b) be the indicator function such that 1_{U_i}=1 if ... 1answer 36 views ### Sampling subsegments from discrete input ranges I have an set of input ranges {[a1, b1], [a2, b2], ...}. Each a and b represent integer ... 1answer 130 views ### Show that Y/Z does not have finite expectation The unit interval (0, 1) is divided into two sub-intervals by picking a point at random from inside the interval. Denoting by Y and Z the lengths of the longer and the shorter sub-intervals ... 3answers 539 views ### How to test uniformity in several dimensions? Testing for uniformity is something common, however I wonder what are the methods to do it for a multidimensional cloud of points. 1answer 147 views ### Estimated distribution of eigenvalues for i.i.d. (uniform or normal) data Assuming I have a data set with d dimensions (e.g. d=20) so that each dimension is i.i.d. X_i \sim U[0;1] (alternatively, each dimension X_i \sim \mathcal N[0;1]) and independent of each ... 2answers 640 views ### What is the expectation of a normal random variable divided by uniform random variable? I have two random variables: x = N(0, \sigma^2) and y =U[0, b]. I need to compute E(x/(1+y)). How does one go about doing this? They are independent so the joint pdf is just the product of ... 3answers 238 views ### Curve smoothing in the presence of non-gaussian uncertainty What options are available for smoothing 2-dimensional real data for which the the ordinate points are real intervals of the form (x_j , [y_{j0} , y_{j1}]) In my case, the data is vague because of ... 1answer 183 views ### Uniform distribution & generation of extreme values in R I'd like to generate a new point which should be uniformly distributed on the interval [a, b) (i.e. including the left extreme value - a and exluding the right extreme value - b). The ... 1answer 376 views ### How to uniformly project a hash to a fixed number of buckets Hi Fellow Statisticians, I have a source generating hashes (e.g. computing a string with a timestamp and other information and hashing with md5) and I want to project it into a fixed number of ... 1answer 415 views ### What is cov(X,Y), where X=min(U,V) and Y=max(U,V) for independent uniform(0,1) variables U and V? Let X=\min(U,V) and Y=\max(U,V) for independent uniform(0,1) variables U and V. What's the covariance of X and Y? Could you develop some calculations, especially regarding the computation ... 2answers 2k views ### How does one measure the non-uniformity of a distribution? I'm trying to come up with a metric for measuring non-uniformity of a distribution for an experiment I'm running. I have a random variable that should be uniformly distributed in most cases, and I'd ... 1answer 160 views ### How to use ppoints to generate points within 0 and 0.05 for qq plotting in R? I ran Tassel3 and I filtered results with p-value not more than 0.05. This way, it is ok to draw a Manhattan plot. However, for a QQ-plot there is a problem. Say I have 40 thousands SNPs, after ... 1answer 252 views ### Marginal of a uniform distribution Given f\left(x|\theta\right)=1/\theta, 0\leq x\leq \theta,L\left(\theta, a\right)=\left(a-\theta\right)^2, and \pi\left(\theta\right)=\theta e^{-\theta},\theta\gt 0 I've seen Problem calculating ... 1answer 785 views ### Covariance matrix of uniform spherical distribution I need to figure out the covariance matrix of a uniform spherical distribution. But there I can't even find a closed form of the distribution. This link says it is \frac{1}{n}\mathbf{I}, where ... 1answer 170 views ### Expected value of min X for bernoulli success? I take a SRS sample of size n from a population of x values ranging from 1 to N. Each selected unit also has a probability p of success or q = 1-p of failure (i.e. the probability of success/failure ... 0answers 108 views ### What is the probability that the kth element falls in a specific interval? The question I'm referring to comes from Stack Overflow: http://stackoverflow.com/questions/8723652/estimating-number-of-results-in-google-app-engine-query In short: With N ordered samples of a ... 2answers 1k views ### Determining sample size for uniform distribution May you help me to decide what is the minimal sample size for a uniform distributed sample. Assume that I've find the sample average, standard deviation and the \alpha. 2answers 812 views ### Problems with extremum of two uniform random variables Here is the problem from the book: Let X = \min(U,V) and Y = \max(U,V) for independent \text{uniform}(0,1) variables U and V. Find the distributions of a) X; b) 1-Y; c) Y-X. I ... 1answer 329 views ### Kolmogorv Smirnov Test in R I want to proof the "Relative Age Effect" of a football team. I have a list of birth dates of the team members (about 20 numbers between 1 and 365, the day of the year). I now want to use the KS-Test ... 0answers 203 views ### Generating random matrices with specific equality constraints Suppose I want to generate a nonnegative n \times n matrix \mathbf A for an odd n (say, n=5 for a good enough example), such that the individual elements are drawn from a uniform ... 1answer 176 views ### How to compute \mathbb P( 3 X_{(1)} \geq X_{(2)}+X_{(3)}) for order statistics of a uniform distribution? I am trying to solve a problem for my thesis and I don't see how to do it. I have 4 observations randomly taken from a uniform (0,1) distribution. I want to compute the probability that 3 ... 1answer 609 views ### How can I sample from a log transformed distribution using uniform distribution? I am transforming an unscaled density function to log scale to avoid underflow issues. BI was performing integration on this function on a grid of values before I used the log transormation, to ... 1answer 230 views ### Estimating upper bound of uniform distribution from max of sample This is actually part of a problem from All of Statistics: X_1, X_2, \ldots, X_n \sim \text{Uniform}(0, \Theta). And Y = \text{Max}\{X_1,\ldots, X_n\}. If you're given that Y > c, can you ... 1answer 300 views ### Mean and variance of a normally distributed random number created from the average of a set of uniformly distributed random numbers An old-fashioned way of generating normally distributed random numbers entailed setting each normally distributed random number equal to the average of a set of uniformly distributed random numbers, ... 1answer 1k views ### Distribution of a ratio of uniforms: What is wrong? Suppose that X and Y are two i.i.d. uniform random variables on the interval [0,1] Let Z=X/Y, I am finding the cdf of Z, i.e.  \Pr(Z\leq z) . Now, I came up with two ways of doing this. ... 1answer 2k views ### Generating random samples from a custom distribution I am trying to generate random samples from a custom pdf using R. My pdf is:$$f_{X}(x) = \frac{3}{2} (1-x^2), 0 \le x \le 1 I generated uniform samples and then tried to transform it to my custom ...
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Recently, I have found in a paper a statement that p-values should be uniformly distributed. I believe the authors, but cannot understand, why it is so.
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### Uniform random variable distribution

This is a homework problem out of the book. It says If $U$ is a uniform random variable on [0,1], what is the distribution of the random variable $X = [nU]$, where [$t$] denotes the greatest ...
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### How to perform goodness of fit test and how to assign probability with uniform distribution? [duplicate]

I have to demonstrate that a generator of VoIP calls generates calls uniformly distributed between callers. In particular the distribution is the uniform (min, max) one where the volume per caller ...
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### Uniform Distribution Test

I've got a data-set which I assume is uniformly distributed. Say I've got N=20000 samples and a suspected p=0.25. This means ...
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### Are there default functions for discrete uniform distributions in R?

Most standard distributions in R have a family of commands - pdf/pmf, cdf/cmf, quantile, random deviates (for example- dnorm, pnorm, qnorm, rnorm). I know it's easy enough to make use of some ...
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### Difference between Excel's RAND(), RAND()*RAND(), etc

I plotted below the standarized results of: RAND() RAND() * RAND() ... RAND() * RAND() * RAND() * RAND() * RAND() * RAND() It seems that the results are getting to zero, is that because you're ...
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### How can I test the fairness of a d20?

How can I test the fairness of a twenty sided die (d20)? Obviously I would be comparing the distribution of values against a uniform distribution. I vaguely remember using a Chi-square test in ...
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### What is the expected MINIMUM value drawn from a uniform distribution between 0 and 1 after n trials?

Assume you draw a uniformly distributed random number between 0 and 1 n times. How would one go about calculating the expected minimum number drawn after n trials? In addition, how would one go ...