# 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.

1,343 questions
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### Finding the expected value for various functions of two independent random variables

Let $X$ and $Y$ be independent random variables with uniform density functions on $[0, 1]$. Find: $E(|X-Y|)$ $E(X)=E(Y)=1/2$, $f_{X,Y}(x,y)=1$ Integrating the region where $x > y$ and using ...
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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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### 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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### 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 ...
### 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 ...