# 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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### Finding density function for uniform distribution

Can anyone help me set this up correctly, please: 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 ...
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### Question about the Irwin-Hall Distribution (Uniform Sum Distribution)

So I have been reading about the Irwin-Hall distribution online, it is a sum of uniform distributions on $[0,1]$, and it seems very interesting: http://en.wikipedia.org/wiki/Irwin%E2%80%...
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### Bivariate and Multivariate Probability Distributions

For my homework for Bivariate and Multivariate Probability Distributions section, I encounter the terms joint density, joint distributed random variable, joint probability, uniform distribution, when ...
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### Interval of non-uniformly distributed set of numbers adjusted that it properly excludes extremes

Let's say I have an interval of numbers from 1 to 9 with the following frequency of distribution: numbers 1, 2 and 3 about 20 occurrences number 6 has 2 occurrences and number 9 has only one ...
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### Looking for a simple bivarate uniform distribution with non-zero covariance matrix

Obviously there are many forms this can take, I'm looking for on that gives an non-zero (off diagonal elements) covariance matrix. Does anyone know of one?
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### Probability that at least one event (out of two uniform RV) happens before two other random events

I recently faced a probability problem that is puzzling me. I would like to ask you if you could help me. I have two random variables X1 and X2 i.i.d with uniform distribution U[64,96] and other two ...
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### Uniformly Distributed ingredients

Suppose we need to make a dish that has three ingredients A, B and C. All are distributed uniformly between [0, 2], [0, 2], [0, 1] respectively. To create the dish, we need 1/4 of A, 1/4 of B and 1/8 ...
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### Finding the joint density of two random variables

Suppose (X,Y) is uniformly distributed over the region { (x, y) : 0 < x < y < 1 }. Find the joint density of (X, Y). I started out by drawing the unit square and filling in the area where 0 &...
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### How to construct a uniform joint distribution

I have a question that is critical to my work, but I am not sure if it is any possible. Assume that you have two uniform random variables X and Y. The product distribution of Z=XY is not a uniform. ...
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### Finding probability of uniform random variable given a condition with another random variable

Suppose X and Y are independent and uniformly distributed on the unit interval (0,1). Find: $$P[Y>\frac{1}{2}\,|\,Y>1-2X]$$ How I approached it was to find the area where $Y > 1 - 2X$, and ...
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### choose a list of words such that have equal letter frequency

I have a big list meaning full Words. surely letter frequency of this word list is different for each letter. Now my problem is to find a way to randomly select words from this word list to a new ...
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### What is the expected time you have to wait until the first bus comes?

 three buses, bus A, B, and C come to a bus stop every hour. The time at which each bus arrives at the stop is distributed as a uniform random variable, i.e., TA,TB,TC ∼ Unif[0,1] hours. The ...
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### Continuous Random Variable - Uniform Median, Exponential Mode

Working on this question: The median of a continuous random variable with CDF $F(x)$ is the value $m$ that guarantees that $$P\{X > m\} = P\{X < m\} = \frac{1}{2}$$ The mode is the ...
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### Summing many non-standard i.i.d. uniform random variables

all! I have looked up a fair bit on this question and learned much about the problem. But haven't been able to get any crisp answers. Sorry, if I'm missing something obvious. I know one can use the ...
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### What is the distribution of $X+Y$ where $X \sim U(0,\frac{L}{2})$ and $Y \sim U(\frac{L}{2},L)$?

I started along these lines: Let $Z = X + Y$ where $\frac{L}{2}< z < \frac{3L}{2}$, then, $$f_{X+Y}(z)=f_{Z}(z) = \int f_{X}(x)f_{Y}(z-x)dx$$ However, I am not sure how to fill in the bounds ...
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### Finding a PMF with random variables

Let $X$ be a discrete random variable that is uniformly distributed over the set of integers in the range $[a,b],$ where $a$ and $b$ are integers with $a<0<b$. Find the PMF of the random ...
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### 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 ...
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### Probability Integral Transformation

I just attended an introductory course on Statistics and we came across the following: I know what random variables, the uniform distribution, etc. are but the notation from the proposition above ...
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### What is the distribution of the impact point of a Random Ray

In the $\displaystyle (O,x,y)$ plane, a random ray emerges from a light source at the point $\displaystyle (-1,0)$, towards the $\displaystyle (O,y)$ axis. The angle with the $\displaystyle (O,x)$ ...
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### Linear Combination of Min and Max of Uniform Random Variables

Let $p$ and $q$ be uniformly distributed on $[0,1]$. Define $x=\min\{p,q\}$, $y=1-\max\{p,q\}$ and $z=1-x-y$. What are the distribution functions of $x$,$y$ and $z$? I've got $F_X(x) = 1 - (1-x)^2$ ...