query: Suppose that $X$ and $Y$ are independent variables of distribution $N(0,1)$, and $Z=\min(X,Y)$. Show that $Z^2 ∼ χ^2 (1)$
positive_passages.docid: 151302
positive_passages.text: If $X$ and $Y$ are independent random variables, with $Z = \min(X,Y),$ prove that $Z^2\sim\chi^2(1),$
negative_passages.docid: 9507
negative_passages.text: How to calculate the distribution of the minimum of multiple exponential variables?
negative_passages.docid: 25618
negative_passages.text: $x,y,z$ independent and uniform random on $[0,1]$, $P(x \geq  yz)$?
negative_passages.docid: 92054
negative_passages.text: $X$ and $Y$ i.i.d., $X+Y$ and $X-Y$ independent, $\mathbb{E}(X)=0 $ and $\mathbb{E}(X^2)=1$. Show $X \sim N(0,1)$
negative_passages.docid: 42266
negative_passages.text: Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
negative_passages.docid: 22586
negative_passages.text: Distribution of $(XY)^Z$ for $(X,Y,Z)$ i.i.d. uniform on $(0,1)$
negative_passages.docid: 30662
negative_passages.text: $x_{1}...x_{n}$ are independent continuous random variables with common distribution function $F(x)$,compute $E(F(x_{(n)})-F(x_{(1)}))$
negative_passages.docid: 46760
negative_passages.text: To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
negative_passages.docid: 95084
negative_passages.text: What is the expected value of $\min\{|X|,|Y|\}/\max\{|X|,|Y|\}$ assuming $X$ and $Y$ are independent?
negative_passages.docid: 153456
negative_passages.text: What is the random variable $Z$ by the notation $Z =X/Y$?
negative_passages.docid: 25654
negative_passages.text: E[X| X>Y] for independent X, Y ~ N(0,1)
negative_passages.docid: 49160
negative_passages.text: Joint distribution of two dependent variables
negative_passages.docid: 6190
negative_passages.text: Maximum/minimum of two random variables is a random variable
negative_passages.docid: 93634
negative_passages.text: X,Y,Z independent and $\sim N(1,1)$. Find $P(X+Y \geqq 3Z)$
negative_passages.docid: 136707
negative_passages.text: Show that if $X$ and $Y$ are independent with the same exponential distribution, then $Z= |X - Y|$ has the same exponential distribution
negative_passages.docid: 116975
negative_passages.text: Given $X$ and $Y$ are independent N(0,1) random variables and $Z = \sqrt{X^2+Y^2}$ from the marginal pdf of $Z$
negative_passages.docid: 39409
negative_passages.text: $X_1,...,X_n$ be independent RVs and $X_i \perp \mathcal F $ for $1\ \leq \forall i \leq n$. Show that $\sigma (X_1,...,X_n) \perp \mathcal F$