The uniform-distribution tag has no wiki summary.
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Uniform probability question
Anyone here that can solve this challenging question that I have?
Let $U \sim U[a,b]$. Suppose $X = U$ and $Y = \frac{1}{2} U$.
Find $P(X \le x, Y \le y)$ for $-\infty \le x, y \le + \infty$.
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2answers
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Combining two identical uniform distributions
Say two random variables, $X$ and $Y$, are such that $X$ ~ $U(0,a)$ and $Y$ ~ $U(0,a)$.
What will the pdf be for $Z$, where $Z=X-Y$?
1
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1answer
28 views
Generating points in rectangle
I am trying to generate $N$ points randomly and uniformly distributed in an $m \times n$ rectangle. How can this be done? I have tried to split the initial rectangle into as many rectangles i could, ...
1
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2answers
54 views
calculate probabilty, Uniform distribution
this is my first question so excuse my unknowing and mistakes:
I was reading a book and just faced this thing:
(1.4) $=P(X\gt Z/2)(Y-X)$
(1.5) $=P(2X\gt Z)(Y-X)$
(1.6) $=\min\{{2X,1\}}(Y-X)$
...
1
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2answers
110 views
Probability density function of a product of uniform random variables
Let $z = xy$ be a product of two uniform random variables, with $x$ having the range $[a, b)$ and $y$ the range $[c, d)$.
What is the probability density function of $z$, and how is it calculated?
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16 views
function of a continuous random variable that is a bernoulli trial?
what is a function of a continuous random variable that is a bernoulli trial?
x= continuous random variable
function(x) = bernoulli trial
examples of continuous random variables: exponential, ...
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0answers
16 views
compare multi-distribution
If
$Y$= a random variable, it is a product of 2 independent uniform distributions [0,1]
$X_1$ = a random variable, it is a independent uniform distributions [0,1]
$X_2$ = a random variable, it is ...
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1answer
63 views
Find coordinates of n points uniformly distributed in a rectangle
I have a rectangle R of width W and height H.
I have N points inside this rectangle.
I need to find an algorithm to position my points in the rectangle in the most uniform way possible (no overlaps, ...
2
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1answer
46 views
A Problem on Uniform Probability Distribution
Consider three independent uniformly distributed (taking values between 0 and 1) random variables. What is the probability that the middle of the three values (between the lowest and the highest ...
4
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1answer
68 views
Why do prime numbers in modulo result in more uniform distributions?
Let us assume a sequence as follows:
$S_{n} = (S_{n-1} * c_{1} + c_{2})\text{ mod } m$
This is the pseudorandom generator found in most programming languages' random function.
It is known that a ...
0
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2answers
45 views
Showing the self energies of $N$ uniformly charged disks is proportional to $N^{3/2}$
How would I go about doing this?
I assume it is some integral I have to solve, but I have no idea what.
(Note:Not a physicist so please excuse incompetence with regard standard notation.)
Context ...
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68 views
Distribution of Sum of Discrete Uniform Random Variables
I just had a quick question that I hope someone can answer.
Does anyone know what the distribution of the sum of discrete uniform random variables is?
Is it a normal distribution?
Thanks!
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0answers
28 views
What is the difference between these two questions?
Consider two independent random variables: X~U(0,1) and Y~U(0,2). Let Z = min(X,Y).
b) Find F$_Z$(z) in terms of F$_X$(.) and F$_Y$(.).
c) Eliminate F$_X$(.) and F$_Y$(.) to find F$_Z$(z).
What is ...
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2answers
73 views
We break a unit length rod into two pieces at a uniformly chosen point. Find the expected length of the smaller piece
We break a unit length rod into two pieces at a uniformly chosen point. Find the
expected length of the smaller piece
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1answer
44 views
How do you generate mean from a uniform distribution between 0 and 1
How do you generate mean from a uniform distribution between 0 and 1
with a sample size of 10? using excel?
Do you have to first generate random numbers from 0 to 1?
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1answer
51 views
Probability of elements in a subset of the original set
Let me try and rephrase the question as an example. I'll use bits since its convenient in this case.
You have 3 bits A, B and C, that have probability 1/2 of being ...
1
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1answer
55 views
In this Cumulative Distribution Function, am I finding the wrong term?
Question I was given: Let V be a uniform random variable distributed over the interval (0,1). Let $\ X = \frac{1}{\sqrt(U)}$. What is the cumulative distribution function and probability density ...
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1answer
78 views
Expected Value Problem (Q-function…inside a function)
I'm working through my textbook for a communications course I'm taking, and this problem is confusing me big time. Like always, the math questions give me the most problems. Maybe I should take the ...
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43 views
Distribution absolutely continuous with respect to Lebesgue [closed]
Let the $X_i$ 's uniformly distributed on [0,1].
For k = 1, ..., n let $X_{k:n}$ be the k smallest of the values of the $X_i$ 's.
What's the distribution function of $X_{k:n}$ ? (and why?)
Why is ...
0
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1answer
56 views
Limit of sum of (continuous) uniform distributions
In my stats courses at university, I've been working on transformations of distributions etcetera.
However, one particular case has intrigued me for a while: the sum of continuous uniform ...
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1answer
63 views
how to calculate probability?
I'm facing difficulty in understanding how they in the book, jumped for (12.13) to (12.14).
what is given is that $b_1$ and $V_2$ are uniformly distributed between $[0,1]$.
I could not post a picture ...
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1answer
113 views
Rao-Blackwell Uniform Distribution
I am having a bit of an argument with my study group about a Rao-Blackwell problem that we have for our statistical theory class.
The problem goes like this:
Let X~U(0,$\theta$), and suppose we have ...
2
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1answer
116 views
Uniform Distribution: finding the probability between two variables
Q: In a uniform density $\mathcal{U}(a,b)$ with $a=-0.025$ and $b=0.025$, what is the probability that an error will be between 0.010 and 0.015?
A: From the density function, I didn't know how $d$ ...
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51 views
Need a proof check for a Uniform Consistent Estimator: Statistical Theory
So I have a homework question that goes:
Let X~U$(0,\theta$). Show that Max($\{X_1, X_2 , \ldots , X_n \}$) is a consistent estimator for $\theta$.
From my class, we were shown that our CDF for Max ...
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1answer
96 views
Uniform Probability Distribution
I have a machine part that have lifetime uniformly distributed between 0 years and 1 year. Whenever a part fails, it is immediately replaced with a new identical part. I know that lifetimes of ...
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1answer
86 views
How to estimate parameters of a uniform distribution?
I have information of the order in which students were classified in regard to their scores in a SAT test. I know the distribution of scores for each student is uniform with support [a,b]. I also know ...
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1answer
229 views
Uniform distribution, Expected value and standard deviation for proportion of observations in a subintervall
$X\sim U(0,1)$. Divide the interval [0,1] into k equal subintervals. Then $X_1$=the number of observtions on the first interval.
Define the new variable $Y_1=X_1/n$, where n is the number of ...
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1answer
244 views
median of a uniform distribution [0,1]
I need to find the distribution of the median from the given distribution, where n is known to be odd.
The formula given in class for this is:
$n=2m+1$ where $m\in\mathbb{N}$
...
2
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2answers
62 views
Comparison of 2 samples from different uniform distributions
Given that $0\le a\le b<1$ and $p$ is uniform on $[a,1]$ and $q$ is uniform on $[b,1]$ then if $p$ and $q$ are random selections then what is the probability that $q>p$?
Edit: I am trying to ...
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Is transfert theorem the best choice in this kind of exercise?
I am studying Probability theory and came to this exercise :
Let $U,V$ be independent uniform random variables over $[0,1]$. Show that $X:=\cos(2\pi V)\sqrt{-2\ln U}$ and $Y:=\sin(2\pi V)\sqrt{-2\ln ...
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136 views
Binomial distribution with Uniform parameter
I have a problem with following exercise (it comes from Geoffrey G. Grimmett, David R. Stirzaker, Probability and Random Processes, Oxford University Press 2001, page 155, ex. 6):
Let $X$ have the ...
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1answer
53 views
Uniform distribution
$X~U(0,1)$ Find $E[\sqrt {X}]$ and the probability density function of $Y$ defined as $Y=X^2$.
I know that $E[Y]=E[g(X)] = \int_a^b g(x)f(x) dx$
I don't know why this question does not meet the ...
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0answers
71 views
Finding Limits of Integration
I have two functions, one depending on $x$ which is
$\frac {1} {2} {\delta(x-5)} + \frac {1} {4}$ which is the combination of a dirac delta function at $5$ and a uniform distribution from $5$ to $7$. ...
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3answers
186 views
Expected number of overlaps between intervals
Suppose $N$ intervals of length $\delta$ are positioned in $[0,1]$. The starting point $l_i$ of each interval is drawn from an uniform distribution, i.e., $l_i \in [0, 1-\delta]$, thus it will ...
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1answer
167 views
equivalence between uniform and normal distribution
The principle of insufficient reason says that all outcomes are equiprobable when we have no knowledge to guess otherwise. I understand this and that this corresponds to uniform distribution. However, ...
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53 views
Distribution of binary digits in moduli
Considering the (infinite) set of all positive integers that are a product of $2$ primes only,
represented in binary $100...01$.
Question: is the distribution of the proportion of $0,1$ digits ...
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1answer
37 views
Consider $X \sim \text{Unif} (\alpha, \beta)$. Find $P(X<\alpha + p(\beta - \alpha))$ Assume $p$ is a constant with $0<p<1$
Consider $X \sim \text{Unif} (\alpha, \beta)$. Find $P(X<\alpha + p(\beta - \alpha))$ Assume $p$ is a constant with $0<p<1$
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2answers
182 views
Finding the mean of a uniform distribution?
I have a random set $\{a,b,c\}$ and a second set $\{e,d\}$
I draw one number first number and one from the second
Letting $X_1$ denote the first number and $X_2$ the second number find, $E(X_1)$ and ...
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2answers
118 views
Prove there exists no uniform distribution on a countable and infinite set.
Can anyone help me with this problem, I can't figure out how to solve it...
Let $X$ be a random variable which can take an infinite and countable
set of values. Prove that $X$ cannot be ...
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1answer
62 views
uniformly distributed question…
I am doing self-study. but I don`t calculate this problem.
so I want to calculating course.
Three numbers are randomly selected and rounded-off to the nearest interger. Let $X_1, X_2, X_3$ denote the ...
0
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1answer
66 views
Distribution probability of elements and pair-wise differences in a sorted list
Suppose a set of $m$ integers from $0$ to $n-1$. The integers are uniformly distributed and unique in the set ($n \gg m$). Then, put all the integers into a list an sort that list:
$$x_0 < x_1 < ...
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1answer
67 views
Order statistic and independence
"If $Y_1, Y_2, ..., Y_n$ are independent, uniformly distributed random variables on the interval $[0, \theta]$, show that $U=Y_{(1)}/Y_{(n)}$ and $Y_{(n)}$ are independent."
I have already found ...
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2answers
130 views
Prove that a function is uniformly continuous
This is my question :
Let $f$ be defined on an interval $I$, and suppose there exists an $M>0$ and $\alpha>0$ such that
$$
|f(x) - f(y)| \leq M|x -y|^\alpha,
$$
for $x,y \in I$. Prove that $f$ ...
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2answers
591 views
Sum of random variables uniformly distributed (0,1) and (0,2)
I'm trying to get $P(0.9<Y<=1.8)$ for the sum of 2 random and uniform values x1,x2 (so that y=x1+x2) where $x1$~$u(0,1)$ and $x2$~$(0,2)$ and I'm trying to do the convolution for it. Seems like ...
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51 views
Calculated probability not matching simulated results
I know that if you take random and uniformly continuous number that are generated by the sum of x1+x2 (so y=x1+x2), the probability $P(0.9<y<=1.8)$ the calculated results are:
y~u(0,1)
= 0.575
...
2
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1answer
119 views
distribution questions
Let $X$ have a uniform distribution $\operatorname{U}(0,1)$, and let
$Y = a + (b-a)X,\, a < b$.
(a) Find the distribution function of $Y$.
(b) How is $Y$ distributed?
Let $X_1$ , $X_2$ be ...
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1answer
53 views
Fetch Minimal Record with Probability
I have three records. the records means intervals,
$A: [1, 5]$
$B: [2, 6]$
$C: [4, 6]$
A, B and C are three humidity sensors. Value of A is between 1 to 5, B is between 2 to 6, and C is between ...
1
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1answer
65 views
Measure the uniformity of distribution of points in a 2D square
I am currently running into this problem: I have a 2D square, and have a set of points inside it, say, 1000 points. I need a way to see if the distribution of points inside the square are spread out ...
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165 views
Two questions about weakly convergent series related to $\sin(n^2)$ and Weyl's inequality
By using partial summation and Weyl's inequality, it is not hard to show that the series $\sum_{n\geq 1}\frac{\sin(n^2)}{n}$ is convergent.
Is is true that ...
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1answer
134 views
Uniform distribution of points on the surface of a circle around a randomly chosen point
In a Monte Carlo simulation i have encountered the following problem: given a unity vector u defining a point A on the surface of a unity sphere, i must randomly determine a new vector forming an ...
