Recent questions tagged uniform-distribution

Let $X$ be a random variable that follows Uniform $(-1,1)$ distribution. The conditional distribution of the random variable $Y$ given $X=x$ is the Uniform( $x^{2}-0.1, x...

Consider a random vector ( $X, Y$ ) such that $Y \sim \operatorname{Uniform}(0,1)$ and the conditional distribution of $X$ given that $Y=y$ is Normal with mean $y^{2}$ an...

Let $(X, Y, Z) \in \mathbb{R}^{3}$ be a point chosen uniformly at random from the unit sphere $S^{2}:=\left\{(a, b, c) \in \mathbb{R}^{3} \mid a^{2}+b^{2}+c^{2}=1\right\}...

The unit interval $(0,1)$ is divided at a point chosen uniformly distributed over $(0,1)$ in $\mathbb{R}$ into two disjoint subintervals.The expected length of the subint...

Let $X$ be a random variable uniformly distributed in the interval $[1,3]$ and $Y$ be a random variable uniformly distributed in the interval $[2, 4]$. If $X$ and $Y$ are...

Consider the quadratic equation $x^2+\dfrac{x}{2}+c=0$, where $c$ is chosen uniformly randomly from the interval $[0,1]$. What is the probability that the given quadratic...

Consider two random variables, (x) and (y), each following a uniform distribution. Specifically, (x) is uniformly distributed over the interval ([1, 3]), and  (y) is unif...

Let $T$ be a subset of $\{1,2, \ldots, n\}$ of size $\frac{n}{2}$, sampled uniformly at random from all subsets of size $\frac{n}{2}$ of the same set $\{1,2, \ldots, n\}$...

Let $\mathcal{F}$ be the set of all functions mapping $\{1, \ldots, n\}$ to $\{1, \ldots, m\}$. Let $f$ be a function that is chosen uniformly at random from $\mathcal{F}...

Initially, $N$ white beads are arranged in a circle. A number $k$ is chosen uniformly at random from $\{1, \ldots, N-1\}$. Then a set of $k$ beads is chosen uniformly fro...

Fix $n \geq 4$. Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2, \ldots, n\}$. The initial probability distribution of...