# 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.

1,341 questions
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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 ...
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 ...