# 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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### Chi2 test on big uniformly random sample [duplicate]

I expect that, in Python with numpy and scipy, scipy.stats.chisquare(numpy.bincount(numpy.random.randint(100, size=1000000))) will return P-value which is very ...
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### Jointly Complete Sufficient Statistics: Uniform(a, b)

Let $\mathbf{X}=x_1, x_2, \dots x_n$ be a random sample from the uniform distribution on $(a,b)$, where $a < b$. Let $Y_1$ and $Y_n$ be the largest and smallest order statistics. Show that the ...
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### Finding pdf of transformed variable for uniform distribution

This is from MITx's Intro to Probability and Statistics course, the problem is on this page. Suppose $X \sim \textrm{Uniform}(0,1)$ and $Y=X^3$. Find the pdf for $Y$. Since it's a uniform ...
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### Detecting relationships between two sets of circular data

I have a set of points $(x_i,y_i)$ where each x & y value is circular & can take on a value from -pi to pi. (The topology of the data is a torus, but I am not sure how relevant that is to the ...
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### Inconsistent results with Monte Carlo solutions to similar problems in probability

I am presently going through the book Fifty Challenging Problems in Probability with Solutions and implementing Monte Carlo solutions to most of the problems in R to get familiar with the language, ...
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### Expected value of MLE of uniform distribution [closed]

Let $X_1,\dots,X_n$ be a simple random sample from $U(0,\theta)$. Let $\hat\theta=X_{(n)}$ be the MLE estimator. How can I find the expected value of $\hat \theta$ and prove that is it consistency? ...
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### Difference between two methods of random point generation [migrated]

In order to do a monte carlo simulation to estimate expected distance between two random points in $n$ dimensional space I discovered the following two similar looking methods to generate random ...
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### Problem involving Scheffe's theorem and asymptotic distribution

If $\{ X_n \}$ are independently and identically distributed $U(0,1)$ random variables and $V_n = n(1 - X_{(n)})$ (where $X_{(n)}$ denotes the $n$th or largest order statistic), then how do I derive ...
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### Continuous uniform random variables convergence question

Let $X_1, X_2, \ldots$ be independent $U(0,2)$ random variables and let $$Y_n = \prod_{i=1}^n \, X_i \;.$$ How do I prove or disprove that that $Y_n$ converges to $0$ almost surely ?
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### setting log-uniform priors in Stan

I have been using Stan for a couple months now and I want to adopt a log-uniform prior on some parameter array real theta[N]. I want to do something like a ...
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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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### Markov Chain Monte Carlo (MCMC): How many samples are needed to get a uniform sample?

I am interested in a general answer although my question is rooted in a specific document. I am using the R package "hitandrun": https://cran.r-project.org/web/packages/hitandrun/hitandrun.pdf On ...
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### When is it appropriate to use the Central Limit Theorem?

I am currently having a read through the Statistical Drake Equation; a method of taking the Drake Equation, letting each number be a uniform random variable, and then applying the Central Limit ...
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### Uniform Distribution on (a 0) MLE

If we have X~U(a,0) where a<0 what is maximum likelihood estimation of a ? I tried to find on internet but I could not find any resource about (a,0) interval, there is resources only for (0,a). Is ...
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### Is it possible to use runif() to generate a vector of random variables with different probabilities? [duplicate]

Here's the question I have to solve: Let X be a random variable with pmf as given: P(X = 1) = 0,1 P(X = 2) = 0,3 P(X = 3) = 0,6. Simulate this distribution ...
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### Uniform Conjugate prior to raleigh

Can someone please explain why the x0 for the posterior is the max of xi in the below solutions? Thanks
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### Histogram bin size to show deviation from uniform distribution

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 ...
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### How to test that sample data is random? [duplicate]

Lets say there's a function that produces a random number between 1-10000. We need to verify that the generated numbers are truly random and that the distribution is uniform. How do we test the ...
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### Statistics Question About Simulating A Dice Roll

A computer programmer is writing a program to simulate a board game. Part of the game involves rolling a fair 6-sided dice. The programmer decides to simulate this roll in the following way. First a ...
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### Uniform distribution MLE

Just a quick question: I know a $U(0, A)$ with density of $1/A$ has as MLE of $X_{max}$, but would a $U(1,1+A)$ have the same MLE that of $X_{max}$? I'm assuming so but just for clarity. Thanks in ...
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### Difference of two Uniform Random Variables [duplicate]

Suppose $A \sim Unif(X, X+1)$ and $B \sim Unif(0,1)$. Find $P(A > B)$. ($A,B$ independent) I started out the following way: $P(A > B) = P(0 > B - A) = P(Z < 0)$, letting $Z = B - A$. ...
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### Sum of uniformly distributed random variables over different intervals?

Let $\{X_i\}_{i=1}^N$ be $N$ random variables uniformly distributed over the intervals $[a_i, b_i]$ respectively. How does the sum: $$\sum_{i=1}^N X_i$$ distribute? This is a generalization of the ...
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### Variance of uniform distribution

I can see how one can compute the variance of a uniform distribution on $[a,b]$ using $$Var[X] = E[X^2] - E[X]^2 = \frac{(b-a)^2}{12}$$ as explained e.g. here: http://www.statlect.com/probability-...
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### Probability the next draw from a distribution is greater than some number given a previous draw

I'm working on a game theory model of incomplete information, where players observe certain attributes via noisy signals. I am looking to solve for two different probability functions, though I think ...
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### Distribution of samples from a uniform distribution [duplicate]

Let's say we are taking $n$ samples from a uniform distribution, that spans from $0$ to $1$. According to the central limit theorem, the mean of the $n$ samples will follow a normal distribution with ...
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### Error in proof of $Y=F(X)$ uniform on $[0,1]$

If we let $Y=F_X(X)$ then $Y\sim U(0,1)$, which is proved in introductory texts in statistics (for example Casella and Berger Statisical Inference p. 54). What is then the error in the "proof" below?...
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### MLE Uniform X∈(N,N+1,…,N+10) [duplicate]

I am trying to find N by MLE for several discrete uniform distributions involving a parmeter N∈Z. If the interval X is defined on is X∈(N,N+1,...,N+10) then I think N^=min{X1,X2,...Xn}.But this isn'...