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Questions tagged [uniform-distribution]

For questions involving random variables uniformly distributed on a subset of a measure space. To be used with [probability] or [probability-theory] tag.

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Moments about the mean of a uniform distribution

I really don't know what needs to be completed here, because I don't understand the parameters of alpha and beta: Show that if a random variable has a uniform density with the parameters alpha ...
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Uniform Probability Distribution 1

A manager of a department store reports that the time of a customer on the second floor must wait for the elevator has a uniform distribution ranging from 2 to 4 minutes. If it takes the elevator 30 ...
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Adjusting a set of random numbers such that they approach a uniform distribution when biased noise is added

A good random number generator, $G$ will produce a sequence of $[0, 1]$ values which are near uniformly distributed as $n$ draws goes to infinity. If I start drawing samples from the random number ...
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26 views

Distribution of distance from origin for uniformly randomly chosen point in circle

So I think I know how to solve (a) correctly for this problem, but I keep getting answers to (b) that don't integrate to be $1$. I think (c) follows straightforwardly from there so (b) is the big ...
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How do I choose the boundaries when I am calculating the marginal $f_X(x)$ of a function?

So I have a question where I have a function: $$f_{X,Y}(x,y)=c$$ for $$(x,y) \in T$$ Where I have seen that $c$ = $\frac{1}{8}$ and where $T$ is the triangular region bordered by $x=0, y=0, x+y=4$....
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3answers
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Probability distribution difficult exercise [duplicate]

I have to solve this exercise and I have no idea how to do it... Help is highly appreciated. We make the following experiment: we ask 2 persons to write one real number from [0, 5] each on a ...
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2answers
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Uniform discrete distribution - time to draw

I have a question about the basic definition of discrete normal distribution. Let's assume I have a machine that draws a number ranging from 1 to 3 from a uniform discrete distribution (the ...
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1answer
49 views

$Y = \frac{X_1 X_2}{X_3}$ where $X_i$ is a uniform random variable

$Y = \frac{X_1 X_2}{X_3}$ where $X_i\sim U(0,1)$ and $X_1,X_2,X_3$ are i.i.d I need to calculate $Var(Y)$ and $Var[Y|X_3=1.7]$ I know that for each $X_i$, $E[X_i]=\frac{1}{2}$ $Var[X_i]=\frac{1}{...
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0answers
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Central moment for a uniform distribution

The probability density function of T is given by $$f(t) = 1/2h \text{, for each } t\in(-h,h) $$ where $h > 0$. Derive an expression for the central moment I used integration and got $\frac{(b-u)...
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1answer
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How to transform a $U(0,1)$ variable to produce a Poisson variable?

Suppose $ X $ is a uniformly distribution over $(0,1)$. How to find transformations $Y=g(X)$ to produce random variables with the Poisson distribution?
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1answer
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Finding density function of random variable

Choose an uniformly distributed random variable $U$ on the unit interval $[0,1]$. Then, what is the probability density function of $Y= \ln(U+ 1)$? I know the density function is the derivative of ...
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1answer
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How can calculate conditional pdf of Y when you dont know about f(y)

X is a uniform distribution on the interval (0,1). Y is a also uniform distribution on the interval (0,x). Its the only information that I could know. Then how can I calculate p(Y|x)? If you teach me, ...
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1answer
1k views

uniformly distributed random variables

Ram and Shyam wanted to meet at a park about 12.30 P.M.. If Ram arrives at a time uniformly distributed between 12.15 P.M. to 12.45 P.M. and if Shyam independently arrives at a time uniformly ...
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Hard demonstration - brilliant minds. I came up with the idea of ​obtaining the limit distribution of an estimator, [closed]

I do not know exactly how to get there, I thought to use the estimate of maximum likelihood but I'm not sure... If $X_1,\ldots , X_n$ are i.i.d. according to the uniform distribution ${\cal U} (0, \...
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understanding the conditional entropy in the case of having uniform distribution?

Would you please help me to understand the conditional entropy in this example which I got stuck in? The example Considers 4 uniformly popular binary vectors, for example; {f1,f2,f3,f4} each with ...
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1answer
23 views

Uniform distributed success probability for a coin

$n\in \Bbb N$. Let $X_1 \sim \text{Uni}_{(0,1)}$ and $X_2 \sim \text{Bin}_{n, X_1}$ conditional on $X_1$. I want to find the distribution function of the law of $X_1$ given $X_2 = k$, i.e. $\Bbb P (...
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4answers
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Frog makes two jumps (uniform distribution)

I received this problem on my exam, although I thought I answered it right, it was marked as wrong. There is a frog on a line. The frog starts from a point 0 and makes two successive jumps: first ...
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2answers
48 views

Variance of x_i chosen from uniformly distributed hypersphere

I'm looking for an expression of the variance of a single component of a point chosen from within a uniformly distributed n-ball with radius r for any n. There are a few proofs showing that ...
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P/1 Actuary Question: Expected value for continuous uniform distribution.

A question reads: A loss random variable has a continuous uniform distribution on the interval $(0, 100)$. A insurance policy on the loss pays the full amount of the loss if the loss is less than or ...
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2answers
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Probability mass function of $ \min(X, Y)$ where $X,Y$ are i.i.d discrete uniform

Let $X$ and $Y$ be two discrete uniform i.i.d random variables distributed over $\{0, 1, 2,\ldots, N\}$. Find the pmf of $Z = \min(X, Y)$. From what I understand, I have to find the joint $pmf$ first,...
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1answer
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Combine standard normal distribution with uniform distribution

I am facing an optimization problem in my business environment that hopefully you guys can help me with. To give you some background on the topic, I am trying to calculate the inventory (called "...
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1answer
61 views

Coverage probability for Uniform$(0, \theta)$

Let $X_1 \dots X_n$ denote a random sample from a uniform $(0, \theta$) distribution. PROBLEM: Compute the coverage probability for the CI: $$\left(\frac{X_{(n)}}{0.95}, \frac{X_{(n)}}{0.25}\right)...
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What is P($X_{1}>X_{2}>…X_{n-1}>X_{n}$)?

Given $X_{i}$, $1 \leq i\leq n$, are independent random variables with uniform distributions on $[0, 1]$, what is P($X_{1}>X_{2}>...X_{n-1}>X_{n}$)? I thought it would be something along the ...
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JPDF for uniform-distribution

you are given that the joint distribution of X and Y is uniform on the region defined by the conditions: $0<x<1$, $x<y<x+1$. Find the correlation coefficient of X and Y My problem with ...
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Alternate characterization of a spatial Poisson point process

Would I be correct to assess that a spatial Poisson point process on some compact, say the $d$-dimensional sphere, can be simulated by first choosing some $n \sim \mathrm{Poisson} (\beta)$ number of ...
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25 views

Probability of uniform distribution with poisson process

Men and women arrive at a store according to independent Poisson processes with hourly rates $\lambda_M$ = 3 and $\lambda_F$ = 4, respectively. Men shop for a time that is uniformly distributed on [0, ...
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1answer
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The probability of heads of a random coin is uniform r.v. P. Find the probability that heads will show?

The question states: The probability of heads of a random coin is a random variable P, uniform in the interval $[0.4,0.6]$. Find the probability that at the next tossing of the coin that heads will ...
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There are $45$ boxes, each of which contains $N$ weapons. If he distributes all the weapons evenly to his $2026$ soldiers,

There are $45$ boxes, each of which contains $N$ weapons. If he distributes all the weapons evenly to his $2026$ soldiers, he would have $2016$ weapons left over. What is the smallest positive value ...
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1answer
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Degree of the minimal sufficient statistic for $\theta$ in $U(\theta-1,\theta+1)$ distribution

Suppose $X_1,X_2,...,X_n$ is a random sample from the Uniform distribution over the interval $(\theta-1,\theta+1)$. By the factorization theorem, it is clear that the order statistics $Y_1=X_\left(1\...
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Consistency of MLE for uniform distribution $U[\theta,1/\theta]$ where $0<\theta<1$

Since the likelihood function of $(X_1,\ldots,X_n)$ is $$L(\theta)=\left(\frac{\theta}{1-\theta^2}\right)^n I(\theta < x_{(1)}) I(\theta < 1/x_{(n)})$$ So the MLE of $\theta$ is $$\hat{\theta}=...
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1answer
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Find probability of combination of two uniform variates [closed]

$X \sim R(0, 2)$, $Y \sim R(0, 5)$, X and Y are independent, I need to find $P(|X-Y| \leq 1)$
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How to find critical value in uniform distribution [closed]

How do you get critical values from uniform distribution p.d.f?? this is the question I got from my teacher enter image description here
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1answer
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Universality of uniform: plugging a random variable into its CDF?

Consider the universality theorem of the uniform distribution. One way to formulate it is the following: Let $F:\mathbb{R}\rightarrow [0,1]$ be a right continuous, increasing function. Then, if $X\sim ...
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2answers
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Probability distribution of a uniform distribution to the third power

I have to find a explicit form of probability distribution of $X^3$, if $X \ \mathtt{\sim} \ U[a, b], \ -\infty < a < b < \infty$. So far I've succesfully done a simpler version, when it's $\...
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1answer
25 views

Expectation of -log(U)

Let $U$ be a uniform distribution on $[0,1]$ 1) Find the distribution function of $V = -log(U)$ (where log is the natural log) 2) Find $E(V)$ What I got: 1) $F_V(x) = P(V<x) = P(-log(U) < x) ...
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Pdf for distance between two uniform random points in a circle

This is my first post in the group and I would be very thankful for any help. I am trying to develop a probability distribution for a performance analysis in my thesis. I am trying to look in to ...
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1answer
123 views

Given pdf of $X$, find a function $U$ that has the same distribution as $X$ where $U\sim Unif (0,1)$

Consider a random variable $X$ having pdf $$f_X(x) = \begin{cases} {3\over{x^4}} & \text{$x \gt 1$} \\ {0} & \text{$x\leq 1$}\end{cases}$$ and consider $U\sim Unif (0,1)$. Give a ...
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1answer
680 views

Proving that a statistic is not sufficient (uniform case).

Let $X=(X_1,...,X_n)$ be i.i.d. $U(0,\theta)$. How to show that $$\frac{2}{n}\sum_{i=1}^{n}X_i$$ is not a sufficient statistic? I have already proven that $\max_{i=1,...,n}X_i$ is a sufficient ...
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On the sum of two random variables with uniform joint distribution on a parallelogram

Given $(X ,Y)$ uniformly distributed over the parallelogram with vertices $(-1,0)$, $(1,0)$, $(2,1)$, $(0,1)$, I'm intrested in the distribution of $Z = X+Y$. Solution The contours of (X, Y) look ...
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1answer
84 views

joint density of two sums of independent random var with common component

Suppose we have three iid draws from a uniform distribution on $[0,1]$. Call these random variables $A, B$ and $C$. Let $X=A+B$ and $Y=B+C$. I have figured out that the density of $X$ (or $Y$) is $$...
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Variant of the Strong Law of Large Numbers

Let $X_1,X_2,\ldots$ be a i.i.d. sequence of random variables with uniform distribution on $[0,1]$, with $X_n: \Omega \to \mathbf{R}$ for each $n$. Question. Is it true that $$ \mathrm{Pr}\left(\...
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Division of two independent uniformly random variable [duplicate]

Given two independent random variable X and Y which both have uniform distribution over[0,1] I want to calculate PDF of $Z =\frac{X}{Y}$ and here is my solution: $\int_{-\infty}^{\infty}zf_X(yz)f_Y(y)...
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Tukey's symmetrical lambda distribution

U ~ Uniform(0,1) $$Z_\lambda = \frac{U^\lambda-{(1-U)}^\lambda}{\lambda} $$ I have to find the first four moments and two ($\lambda_1,\lambda_2$) such that they have the same four moments.
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What is the distribution of the modulo of a uniformly-distributed random variable

This feels like something that's easy to answer, but maybe not. (For the record, this isn't homework from school, it's to settle an argument I'm having with a colleague.) I have a random variable $X$ ...
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2answers
25 views

Shortcut to finding the distribution of a specific random variable

Question: A dice is rolled 3 times. Let X denote the maximum of the three values rolled. What is the distribution of X (that is, P[X = x] for x = 1,2,3,4,6)? You can leave your final answer in terms ...
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1answer
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Probability norm less than threshold in unit ball

From exercise 2.4 in Elements of statistical learning, studying this solution : http://tullo.ch/static/ESL-Solutions.pdf Points $x_{i}, i=1..N$ are uniformly distributed in a p-dimensional unit ball ...
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1answer
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How to compute a conditional expectation

I want to compute a conditionnal expectation, i know that $Z=(Z_1,\ldots,Z_p)'$ where $ Z_j=\Phi ^{-1}(U_j)$ with $Z \sim N(0,R(\theta))$ and $R(\theta)$ the $p \times p$ positive definite ...
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2answers
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Generating Standard Uniform random variable

The book I am following has a problem that states: Let $U$ be a Standard Uniform random variable. Show all the steps required to generate Then proceeds to list off questions on generating other ...
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multiple distributions

Anybody can solve this question that will help me a lot. Losses due to earthquakes in a specific region are distributed uniformly in ($1MM, $5MM) and also number of earthquakes is distributed ...