What is Uniform distribution: Definition and 71 Discussions

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, a and b, which are the minimum and maximum values. The interval can either be closed (e.g. [a, b]) or open (e.g. (a, b)). Therefore, the distribution is often abbreviated U (a, b), where U stands for uniform distribution. The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable X under no constraint other than that it is contained in the distribution's support.

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  1. C

    Uniform distribution on simplex

    How can we show that Dirichlet distribution with parameters α = (α1, ..., αK) all equal to one is uniformly distributed on a K-dimensional unit simplex?
  2. C

    Uniform distribution on high dimensional space

    I would like to ask how to define a uniform distribution on a high dimensional spaceR^n. What is the density of such distribution?
  3. G

    Expected value of the log of a uniform distribution

    Homework Statement How to calculate the expected value of the log of a uniform distribution? Homework Equations E[X] where X=ln(U(0,1)) The Attempt at a Solution integral from 0 to 1 of a.ln(a) da where a = U(0,1) = -1/4 However I know the answer is -1
  4. S

    MLE, Uniform Distribution, missing data

    I would like to determine the MLE for k in U(0,k) where U is the uniform pdf constant on the interval [0,k] and zero elsewhere. I would like this estimate in the case of missing data. To be specific, what is the MLE for k given the three draws X={1,3,*} where * is unknown.
  5. I

    Uniform Distribution, Absolute Value

    Homework Statement Find the CDF of |X|, given that X is a random variable, uniformly distributed over (-1,3). Is |X| uniformly distributed? If yes, over what interval?Homework Equations The Attempt at a Solution I found so far that: Setting Y=|X| Then: Y \in (1,3) F_{Y}(y)=P\left\{Y\leq...
  6. E

    Finding PDF of uniform distribution

    Homework Statement Let X be a uniform random variable in the interval [0,1] i.e., X = U [(0,1)]. Then a new random variable Y is given by Y= g(X), where g(x)= -a. ln(x). Show that Y is exponentially distributed. What is the mean of Y? Homework Equations fX(x) = 1/ lambda . exp (-x/...
  7. D

    Uniform Distribution with Conditional Probability

    Homework Statement So I just took a probability test and I'm having a hard time with the fact that my answer is wrong. I've done some research online and I believe I am correct, I was hoping to get some input. I'm new to using LaTeX so sorry if it's sloppy. Thanks! Problem: Suppose that the...
  8. G

    Sum of independent uniform distribution conditional on uniform

    Homework Statement Let X and Y be independent and normal, then we know that It must be the case that X+Y and X are jointly normal Therefore we can apply the projection theorem: which states that if A and B are jointly normal then VAR(A|B)=VAR(B)-\rho^2VAR(B) , apply the theorem to A=X+Y, B=Y...
  9. A

    Expectation of an Uniform distribution maximum likelihood estimator

    Hi had this question on my last "Statistical Inference" exam. And I still have some doubts about it. I determined that the maximum likelihood estimator of an Uniform distribution U(0,k) is equal to the maximum value observed in the sample. That is correct. So say my textbooks. After that the...
  10. B

    Using uniform distribution to determine the side of a die

    Homework Statement Let U have a U(0, 1) distribution. a. Describe how to simulate the outcome of a roll with a die using U. b. Define Y as follows: round 6U + 1 down to the nearest integer. What are the possible outcomes of Y and their probabilities? Homework Equations A continuous...
  11. K

    Uniform distribution on sphere

    Hello I am trying to make a uniform distribution of points on a sphere. I can find the answer \theta=\pi R_1 \phi = arccos(1-2R_2) where R1 and R2 are uniformly distributed random numbers between 0 and 1. To me, it feels like \theta=\pi R_1 sin(R1) \phi = 2\pi R_2 should also give...
  12. I

    Why does the sun have non uniform distribution of magnetic fields?

    I recall the non uniform distribution of magnetic fields is the reason sun spots occur. Why are sun spots more predominant about the equator as well?
  13. C

    Uniform distribution find E(Y|x)

    This is the question: If X and Y have a uniform distribution over the circle x^2 + y^2 \leq 9 find E(Y|x). Can someone please explain to me, how to answer this question. You guys don't have to give me a solution, but a hint would be nice because I have no idea where to start. Thank you :smile:
  14. belliott4488

    Probability of N or more from uniform distribution

    If I have N objects uniformly placed at random in a 1-d box of length b, how do I calculate the probability of finding one or more objects in a given length? Here's what I mean: I assume a uniform probability density of 1/b, that is, P = 1/b for 0<x<b and P = 0 everywhere else. I now place N...
  15. E

    Random Unit Vector From a uniform Distribution

    Hi, I have encountered the following problem in my research. As I do not have a strong background in probability theory, I was wondering if anyone here could help me through the following. I would like to know how one makes rigorous the problem of randomly choosing a unit n-dimensional...
  16. nicksauce

    Large numbers and standard deviation for a uniform distribution

    In doing a problem, I considered N (a large number, in the range 100,000-1,000,000) raindrops, falling into A (fixed at 100) segments on a roof, distributed using a random number generator I programmed. In considering the number of raindrops that fell into a given segment, the average would be...
  17. K

    Uniform Distribution (Probability)

    Homework Statement Let X be a discrete random variable with the p.m.f given in the following table: x 10 20 30 40 p(x) .25 .2 .4 .15 Suppose you can generate a random value, u, from a uniform(0,1)...
  18. I

    E-field due to a large circular plane of uniform distribution

    E-field due to a large circular plane of uniform distribution! Hi Imagine i have a circular disc of radius R with uniform charge density, and a small charge x meters away from its center. The idea is to calculate the e field for this charged disc on the small charge. I can solve this problem...
  19. C

    Uniform Distribution: What If b-a < 1?

    If X ~ U(a, b) then f(x) = 1/(b-a) but what if b-a is less than 1 for instance if X ~ (.5,1) then f(x) = 2? I'm a bit confused. Any help would be appreciated.
  20. J

    Finding PDF of Y from Uniform Distribution of X1-Xn

    Suppose X1, . . . ,Xn are independently and identically from the uniform distribution on [0, 1]. Find the probability density function of Y = min[X1, X2, ... , Xn]. I do not know how to formulate this problem. I know that the pdf has to be some integral, but no clue so far.
  21. M

    How to visualize joint uniform distribution

    Lets say you have X and Y, where the joint density function for X and Y is uniform over the region defined by 0<=x<=y<=L, where L is some positive constant. The question asks for the expected value of the squares of X and Y. I am having trouble visualizing what such a distribution would...
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