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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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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Finding probability of $U$ independent of joint pmf $f_(X,Y)(x,y)$ - meaning?

Given two random variables, $X$ and $Y$, with a joint pmf: $f_{(X,Y)}(x,y) =$ \begin{array}{ll} 0.3 ,\text{if} \space (x,y) = (3,0) \space \text{or} \space (0,6) \\ 0.2, \text{if} \space (...
130 views

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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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 ...
106 views

What is the distribution of the number of occurrences of a given integer, in repeated samples drawn from Uniform Integer [1, N] distribution?

If I draw M repeated samples from Uniform Integer Distribution on [1,N], what will be the distribution of the number of times a given integer chosen among the integers 1,2,...,N appears in my M ...
248 views

Test of uniform distribution using KS-test and chi square in R

I want to test if a given sample $x$ of $n = 500$ continuous observations is uniformly distributed on a given interval of $[a,b]$ ($a = min(x)$ and $b = max(x)$). Therefore I would like to compare the ...
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Generating three random numbers from normal distribution using 3 independent uniform numbers

Each of the variables A,B,C follows a normal distribution with E(A)=E(B)=E(C)=1,V(A)=1,V(B)=2,V(C)=4. Correlation between A-B=0.2,B-C=0,AC=0.8. We are given three independent uniform (on[0,1]) random ...
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UMVUE of $\cos\theta$ when $X_i\sim U(0,\theta)$

$X\sim U(0,\theta)$. To find the umvue of $\cos\theta$ is it enough to find the umvue of theta and substitute for it. Umvue of $\theta$ being $(n+1)X_{(n)}/n$, is the answer $\cos (n+1)X_{(n)}/n$?
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What is the posterior distribution of a Bernoulli prior that gets updated with a continuous uniform signal?

I'm trying to figure out what the distribution of the posterior is after I update a Bernoulli prior with a continuous uniform signal, say: P(D=G|u)=x where D{G,I} and u is uniformly distributed on ...
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Unclear “mathematical notation” in a polynomial

Although, the Enigma here is a protocol for enhancing the privacy in blockchain; however, the question is about mathematical notation, where we want to calculate the coefficients in a polynomial. ...
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Prove the maximum order statistic $X_{(n)}$ is a minimal sufficient statistic for the uniform$(0,\theta)$ family using a particular theorem

I'm doing Exercise 6.26 in Casella and Berger's Statistical Inference, and I'm trying to prove the following: "Use Theorem 6.6.5 to establish that, given a sample $X_1,...,X_n$, the maximum order ...
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Discrete uniform vs binomial distribution

Situation: a box contains N balls numbered $1,2...,N$. $N$ unknown. $n$ balls drawn using SRS with replacement and number recorded. A random variable $X$ is defined as the number recorded on $ith$ ...
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Expected outcome of a process following a uniform distribution [closed]

A gambler is playing a game of roulette. There are $37$ possible outcomes, each numbered from $1$ to $37$. The probability of rolling any outcome is the same for each outcome. One game of this ...