Questions tagged [uniform]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
126 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 ...
3
votes
1answer
1k 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 ...
1
vote
1answer
253 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 ...
9
votes
1answer
500 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 other....
2
votes
2answers
2k 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 ...
4
votes
3answers
748 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 ...
3
votes
1answer
768 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 ...
3
votes
2answers
2k 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 ...
0
votes
1answer
682 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 ...
4
votes
0answers
146 views

What is the probability that the $k$th element falls in a specific interval?

The question I'm referring to comes from Stack Overflow: https://stackoverflow.com/questions/8723652/estimating-number-of-results-in-google-app-engine-query In short: With $N$ ordered samples of a ...
1
vote
2answers
6k 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 $\alpha$.
0
votes
1answer
3k 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 ...
9
votes
1answer
284 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 X_{(1)}\...
7
votes
1answer
2k 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 ...
3
votes
1answer
754 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 ...
1
vote
1answer
780 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, ...
8
votes
1answer
7k 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. ...
4
votes
2answers
2k views

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 ...
6
votes
3answers
8k views

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 ...
3
votes
1answer
5k views

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 ...
4
votes
4answers
1k views

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 ...
2
votes
2answers
2k views

What would the calculated value of the standard deviation of a uniform distribution be?

A colleague wants to compare models that use either a Gaussian distribution or a uniform distribution and for other reasons needs the standard devation of these two distributions to be equal. In R I ...

1
9 10 11 12
13