Uniform distribution Definition and 71 Threads

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?

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

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.

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...

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/...

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...

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...

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...

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...

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...

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?

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:

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...

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...

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...

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)...

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...

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.

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.

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...