# 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.

1,315 questions
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### Generating three random numbers from normal distribution using 3 independent uniform numbers

Each of the variables A,B,C follows a normal distribution with E(A)=E(B)=E(C)=1,V(A)=1,V(B)=2,V(C)=4. Correlation between A-B=0.2,B-C=0,AC=0.8. We are given three independent uniform (on[0,1]) random ...
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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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### Acceptance and rejection sampling.

The standard logistic distribution function F given by $F(x) = 1/(1+e^{-x}) , x$ is a real number. How to generate a random sample of size 10000 using acceptance-rejection sampling using standard ...
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### Interpretation of sentence to pdf

Just a quick question on interpreting what this pdf looks like: Bacteria are distributed randomly and uniformly throughout river water at the rate of $\lambda$ bacteria per unit volume. n test tubes ...
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### uniform distribution with interval (0,2) and sample 12

Q): Suppose that you wish to sample $12$ observations randomly from a uniform distribution on the interval $(0,2)$. An approximate value of the probability that the average of your sample will be less ...
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### Given a function that generates random numbers with uniform distribution over (0, 1) find a function to generate numbers with Bernoulli distribution.

If we have a continuous random variable $X$ with uniform distribution over $(1, 0)$ we can find functions that generate numbers with other distributions using this random variable. For example if we ...
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### Probability that Alice and Bob keep dating infinitely often

I solved the following problem. I would appreciate it if you can please provide feedback and let me know if I have made any mistakes. Problem statement: Online dating: On a certain day, Alice ...
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### P(X>Y) when X and Y are continuous uniform distribution

Suppose $X$ and $Y$ are continuous uniform random variables. If $X \sim U[a,b]$, $Y \sim U[c,d]$ and $[c,d] \subset [a,b]$ find the probability that a random $X$ value is greater than a random $Y$ ...
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### Height of uniform distribution?

If X follows a uniform distribution in the interval [2, 7], what is the height of the probability density function (pdf) at x = 4? I'm new to Probability & Statistics and will appreciate any help!...
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### Uniform distribution over the unit disk

Suppose that $U_1$ and $U_2$ are independent, and identically and uniformly distributed over the unit disk, i.e., for $i = 1,2$, $U_i = (X_i, Y_i)$ and the joint density is f_{(X_i,...
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### Can sum of two random variables be uniformly distributed

Say $X$ and $Y$ are two random variables where $X\in [-\alpha,\alpha]$, $Y\in [-\alpha,\alpha]$ and $Z=X+Y$. Is it possible to find two independent random variables with certain pdf (not necessarily ...
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### Compute $P(X_{(2)} ≤ 3X_{(1)})$ by using the integration technique

Suppose that $X_1,X_2,X_3.X_4$ are independent $U\in(0,1)$-distributed random variables and let $(X_{(1)}X_{(2)}X_{(3)}X_{(4)})$ be the corresponding order statistic. Compute $P(X_{(2)} ≤ 3X_{(1)})$ ...
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### Conditional expectation of uniform random variable given order statistics [closed]

Assume X = $(X_1, ..., X_n)$ ~ $U(\theta, 2\theta)$, where $\theta \in \Bbb{R}^+$. How does one calculate the conditional expectation of $E[X_1|X_{(1)},X_{(n)}]$, where $X_{(1)}$ and $X_{(n)}$ are ...
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