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. WMDhamnekar

    I Computing the expectation of the minimum difference between the 0th i.i.d.r.v. and ith i.i.d.r.v.s where 1 ≤ i ≤ n

    Problem :Let ##X_0,X_1,\dots,X_n## be independent random variables, each distributed uniformly on [0,1].Find ## E\left[ \min_{1\leq i\leq n}\vert X_0 -X_i\vert \right] ##. Would any member of Physics Forum take efforts to explain with all details the following author's solution to this...
  2. M

    A Uniform distribution setup

    A random variable is distributed uniformly over a circle of radius R. What does the cdf ##F(x,y)## look like as a function of the Cartesian coordinates? The pdf can be expressed as ##f(x,y)=\frac{\delta(\sqrt{x^2+y^2}-R)}{2\pi R}##, where ##\delta## is Dirac delta function. Integration is...
  3. M

    Intersection of two line segments from uniform distribution

    Hi, I found this question online and made an attempt and would be keen to see whether I am thinking about it in the right manner? Question: Find the probability of two line segment intersecting with each other. The end points of lines are informally sampled from an uniform distribution...
  4. D

    Uniform distribution of two random variables

    i did not get how the professor came to such result. In particular: in order to evaluate P[x+y<=z] solved a double integral of the joint density. What i am not getting is did i choose the extreme of integration in order to get as result ##\frac {z^2} {2}##
  5. L

    MHB Understanding the CDF and PDF of a Uniform Distribution for Y

    I need guidance on part c, finding the cdf/pdf of Y. I understand that for X>3, Y=6-X and for X<3, Y=X. For X = 3, Y=3 For part b, I got P(Y>y)= (3-y)/3, for 0≤y<3 Now for part c, I know P(Y>y) relates to the cdf. But the definition of cdf relates to P(Y<y), so I'm guessing I have to do...
  6. thebosonbreaker

    B Continuous uniform distribution - expected values

    Hello, I am currently stumped over a question that has to do with the continuous uniform distribution. The question was taken from a stats exam, and while I understand the solution given in the mark scheme, I don't understand why my way of thinking doesn't work. The problem is: The sides of a...
  7. R

    Uniform distribution and standard deviation

    +(3/2) standard deviations from the mean = \frac {a+b}{12} + \frac{\sqrt3}{4} (b-a) -(3/2) standard deviations from the mean = \frac {a+b}{12} - \frac{\sqrt3}{4} (b-a) \frac {1}{b-a} \int_a^{\frac {a+b}{12} - \frac{\sqrt3}{4} (b-a)} dx = m_1= \frac {(-11+3\sqrt3)a + (1-3\sqrt3)b}{12(b-a)}...
  8. fight_club_alum

    Uniform distribution of charge and work needed

    Homework Statement A charge of +3.0 μC is distributed uniformly along the circumference of a circle with a radius of 20 cm. How much external energy is required to bring a charge of 25μC from infinity to the centre of the circle? a . 5.4 J b. 3.4 J <- answer c. 4.3 J d. 2.7 J e. 6.8 J=...
  9. T

    Continuous uniform distribution function

    Homework Statement Can someone explain why f(x) = 1/(b-a) for a<x<b ? Homework EquationsThe Attempt at a Solution shouldn't it be 0? since its a continuous random variable and so that interval from a to b has an infinite number of possible values?
  10. BobblyHats97

    If X ∼ Uniform(−1, 1) find the pdf of Y = |X|

    This question is killing me. I know the graph is non-monotonic so i have to split up finding F(Y) for -1<Y and Y<1 but then what do I do with the modulus? >.< Any help would be greatly appreciated! Thank you so much x
  11. L

    A quick Question on Joint Uniform Distribution

    Hi, I have a quick question. If both X and Y are uniformly distributed on the unit interval [0, 1]. Can we prove that the joint distribution of (X, Y) is uniform on the unit square [0, 1]×[0, 1]? Do we need any condition to ensure the result, such as Independence between X and Y? Thanks.
  12. M

    How do I calculate an area of joint uniform distribution with domain

    This technically isn't a coursework or homework problem: I have a uniform Joint density function for the lifetimes of two components, let's call them T1 and T2. They have a uniform joint density function, both are positive it follows, and the region is 0<t1<t2<L and L is some positive constant...
  13. diracdelta

    Probability density function of uniform distribution

    Homework Statement Random variable X is uniformly distributed on interval [0,1]: f(x)=\begin{cases} 1 & \text{ if } 0\leq x\leq 1\\ 0 & \text{ else} \end{cases} a) Find probability density function ρ(y) of random variable Y=\sqrt{X} +1 I tried like this. Is it good, if no why not...
  14. CAH

    Statistics uniform distribution problem

    It's hard to type this out as there is a diagram and notation I can't find on the key board so I've attached an image of the question and answer. I've explained my solution below however I've also attached an image if it's too confusing with the lack of symbols! Problem involves uniform...
  15. D

    Uniform distribution- probabilities

    Hello, I am stuck at this exercise: 1. Homework Statement X ~ U(0, a), a > 0 and Y = min(X; a=2). - Find the cumulative distribution function of Y -Is the variable Y continuous ? Homework Equations 3. The Attempt at a Solution [/B] The density function for X is f(t)= 1/a if 0≤t≤a , 0...
  16. H

    Uniform Distribution Probability

    Homework Statement The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0,12]. You observe the wait time for the next 95 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2...
  17. A

    Normal distribution or Uniform distribution

    Hello, I have two jobs,Normal distribution with mean of 4.5 minutes and standard deviation of 1.5 minutes for type 1 and uniformly distributed between 1 and 3 minutes for type 2
  18. tom.stoer

    No uniform distribution on infinite sets

    What exactly prevents us from ruling out a uniform distribution on infinite sets? To be more precise, why are distributions and limits like \int_{-\infty}^{+\infty}dx\,\lim_{\sigma\to\infty}f_{\mu,\sigma}(x) = 1 \int_{-\infty}^{+\infty}dx\,\lim_{\Lambda\to\infty}\frac{1}{\Lambda} \chi_{[a,a+L]}...
  19. D

    Probability Problem (Uniform Distribution)

    1. A harried passenger will miss by several minutes the scheduled 10 A.M. departure time of his fight to New York. Nevertheless, he might still make the flight, since boarding is always allowed until 10:10 A.M., and extended boarding is sometimes permitted as long as 20 minutes after that time...
  20. M

    Gaussian signal, extract uniform distribution of values

    Hello, From an offset zener diode breakdown circuit, I have collected a set of bytes from an ADC. The values distribute normally as integers between 0 and 1024 with a mean of 512. I would like to use the data to create a set of random integers that distribute uniformly. So far, I have...
  21. F

    Matlab continuous uniform distribution

    Homework Statement Generate 100 data points from a continuous uniform distribution with mean = 10 and variance = 4 Homework Equations u = (a+b)/2 var = (b-a)^2 / 12 r = a + (b-a).*rand(100,1); The Attempt at a Solution points = 100 m1 = 10 v1 = 4 syms a b [a...
  22. S

    Uniform distribution Probability

    John is going to eat at at McDonald's. The time of his arrival is uniformly distributed between 6PM and 7PM and it takes him 15 minutes to eat. Mary is also going to eat at McDonald's. The time of her arrival is uniformly distributed between 6:30PM and 7:15PM and it takes her 25 minutes to eat...
  23. D

    Parametric hypothesis, uniform distribution

    Homework Statement We are given a sample of size 100. After some tests (histogram, Kolmogorov) we deduce the sample X is distributed uniformly. The next task is to presume the parameters are equal to values of your choice, and test if such hypothesis is true. Homework Equations The Attempt at...
  24. P

    Statistics Problem - Uniform Distribution

    Hi, The question is: http://puu.sh/5GX2G.jpg http://puu.sh/5GX2G.jpg I am not exactly sure what the question is asking. Here is the answer/solution: http://puu.sh/5GX68.png But I am not sure what is going on. Could someone please explain what exactly the question is asking...
  25. B

    Uniform distribution of charge on a plane and on a bar: conditions to

    On the plane z=0 there is a superficial charge distribution such that \sigma is constant. Near to the plane, there is a bar, charged uniform with total charge q. At the extremities the bar has two constraints, so it can't turn. If I want to find the constraints force and the force momentum...
  26. MathematicalPhysicist

    Uniform distribution on the n-sphere.

    Hi, I have the next RV: $$\underline{W}=\frac{\underline{X}}{\frac{||\underline{X}||}{\sqrt{n}}}$$ where $$X_i \tilde \ N(0,1)$$ It's a random vector, and I want to show that it has a uniform distribution on the n-sphere with radius $$\sqrt{n}$$. I understand that it has this radius...
  27. S

    The shorter side can be distributed by X~U[0,10]

    http://gyazo.com/b031e9d54f9512e5a583a4ed0ea28a0a the answer is 2/3: my attempt: one side X~U[1,7] the longer part of this side, call Y, where Y~[4,7] P(Y>6) = 1/3 don't see how they got 2/3, they have 3 different methods in the answers, but none doing my method. I'm...
  28. L

    Showing a random Variable has a continuous uniform distribution

    f(x)=1, θ-1/2 ≤ x ≤ θ+1/2 Given that Z=(b-a)(x-θ)+(1/2)(a+b) how would you show that Z has a continuous uniform distribution over the interval (a,b)? Any help would be much appreciated.
  29. J

    Uniform Distribution over n and its limit

    Homework Statement Let Yn be uniform on {1, 2, . . . , n} (i.e. taking each value with probability 1/n). Draw the distribution function of Yn/n. Show that the sequence Yn/n converges in distribution as n → ∞. What is the limit? Homework Equations So Yn has c.d.f Yn(x) = |x|/n where |x| is...
  30. P

    Non-applicability of uniform distribution formulae?

    I have tried finding a table's length using two methods. Both should be applicable, as using a ruler implies uniform distribution, does it not? The first method involved calculating the mean length from a set of measurements, finding the variance, and substituting it in the formula for the total...
  31. I

    Uniform Distribution on unit Circle

    I keep reading that a random vector (X, Y) uniformly distributed over the unit circle has probability density \frac{1}{\pi}. The only proof I've seen is that f_{X,Y}(x,y) = \begin{cases} c, &\text{if }x^2 + y^2 \leq 1 \\ 0 &\text{otherwise}\end{cases} And then you solve for c by integrating...
  32. I

    Probability - Uniform distribution word problem.

    Homework Statement Jake leaves home at a random time between 7:30 and 7:55 a.m. (assume the uniform distribution) and walks to his office. The walk takes 10 minutes. Let T be the amount of time spends in his office between 7:40 and 8:00 a.m.. Find the distribution function F_T of T and draw...
  33. K

    Uniform distribution - Independent Randmo variables?

    Hi guys, I have this doubt but i am not sure, if i have an uniform distibution can i conclude that the events or random variables are independent? Thank you
  34. R

    Finding the prob. in a continuous uniform distribution (z values)

    Homework Statement Homework Equations The Attempt at a Solution I understand that all i need to do is plug these two points into the formula and subtract to get the correct area, but i am not provided a mean or variance as i normally am, so I'm at a loss.
  35. S

    Discrete uniform distribution prrof

    Hello, I'm currently in high school and going over discrete uniform distribution, and we've come across this formula. I'm curious if anyone could show me how the formula is true, as when I asked my teacher he just said that it'll confuse the class and we don't need to know why it's true. If...
  36. M

    Confidence interval for estimated mean of (discrete) uniform distribution

    Say that there is a random variable X ~ U(a,b) where U is the discrete uniform distribution on integers on the interval [a,b]. Sample n such variables with the same (unknown) parameters a and b. Using those samples it's possible to estimate the mean either by taking the sample mean (sum the...
  37. J

    How can I solve this uniform distribution question?

    Homework Statement http://www.xtremepapers.com/Edexcel/Advanced%20Level/Mathematics/Subject%20Sorted/S2/S2%202008-06.pdf Question 1(d) Homework Equations The Attempt at a Solution So I know this is a conditional probability question. Now I would have said P(X>8) / P(X=5) because it...
  38. S

    Transformation of the uniform distribution

    Homework Statement I am told that X is a random variable with uniform distribution over [0,1] I need to find the mean and variance of log(X) 2. The attempt at a solution I assume I must find the pdf of log(X) so I did this as follows; Let Y=log(X) Then to find the cumulative...
  39. W

    How to verify a uniform distribution on n-sphere

    suppose we have many dots on a unit n-sphere i suspect that they satisfy the uniform distribution but how to verify this?
  40. T

    Uniform distribution transform: e^2x

    X is a uniformly distributed random variable on a [-1, 1] range. (i.e. X is U(-1, 1)) Find the distribution of e^2X: I feel like it has something to do with the uniform's relation to exponential function, but i get stuck. I begin by using inverse transform: Fy(y) = Fx[ln(y)/2] fy(y)...
  41. Barnak

    Uniform distribution on a toroidal surface

    I'm not sure this is the right thread to post my problem : I'm trying to define a uniform distribution on the toroidal surface associated to a dipolar magnetic field (or electric). More specifically, the surface (in 3D euclidian space) is parametrised as this, using the usual polar...
  42. B

    Transforming a uniform distribution into a binomial

    Homework Statement Let X~UNIF(0,1). Find y = G(u) such that Y = G(U)~BIN(3,1/2) Homework Equations The Attempt at a Solution after a bit of searching/reading, i found how to do this with a continuous distribution (the problem i had was an exponential, so i took the inverse)...
  43. L

    Find Confidence Interval w/o Formula: Uniform Distribution

    i am given a set of numbers. I have already found the mean, standard deviation, etc. i am now asked to find the confidence interval. but was not given a formula in order to compute this. does anyone know one?
  44. Oxymoron

    Uniform Distribution Transformation

    Homework Statement A random variable X is distributed uniformly on [-1,1]. Find the distribution of X^2, its mean and variance. The Attempt at a Solution Define a transformation of random variable as Y=X^2. Problem is that the transformation function is not monotonic on the range. If it...
  45. S

    Question on Probability & Uniform Distribution.

    Suppose a sample of random size N is taken from the continuous uniform(0, θ) distribution, and N has a discrete distribution with p.m.f. P (N = n) = 1/(n! (e − 1) ) for n = 1, 2, 3, . . . . Determine the distribution of the i) first order statistic (the minimum) of X1 , X2, . . . , XN ...
  46. D

    Find the PDF of W = X + Y + Z on a Uniform Distribution

    I am stumped. I have that W=X+Y+Z and that S=X+Y These are all X, Y, & Z and Independent and Uniformly Distributed on (0,1) I found the pdf of S to be (Assume all these < rep. less than or equal to): S when 0<S<1 2-S when 0<S<1 So I continued: To do pdf of S+Z=W I figured...
  47. M

    Uniform distribution on the disc

    Homework Statement consider a disc of radius 1 in the plane D in R^2 D = {(x,y) in R^2 | x^2 + y^2 <=1 } what is the marginal pdf of x and y Homework Equations The Attempt at a Solution so the joint distribution of xy is 1/Pi for x^2 + y^2 <=1 right? but how exactly? "density"...
  48. M

    Uniform distribution of a disc

    Homework Statement Consider a disc of radius 1 in the plane D in R D = {(x,y) in R | x^2+y^2 <= 1} write the marginal pdf of x and y Homework Equations The Attempt at a Solution so the joint pdf is 1/Pi for x^2 + y^2 <= 1 <- correct? but how to I get the marginal pdfs?
  49. R

    Uniform Distribution Expected Value

    Homework Statement If X~(-5,5) find E[||X|-2|] Homework Equations If a variable is distributed uniformly then f(x) = 1 / (b-a), with a mean of (a+b)/2. If x~u, then y~u. The Attempt at a Solution I think I should change the variable, so y = |X| - 2, and then find E[|y|]. So if I...
  50. L

    Uniform distribution of a disc

    1. Homework Statement Here is the link to the old thread, https://www.physicsforums.com/showthread.php?t=349730 i tried posting but it doesn't seem active. I don't understand how they get the second pdf as i tried it and got the first pdf. I also don't know how to do the double integral as...
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