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2 votes
2 answers
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Determine density of $\min(X,Y)$ and $\max(X,Y)$ for independently uniform distributed variables

Two independent random variables, $X$ and $Y$, are uniformly distributed on the unit interval $(-1,1)$. Determine the density for $U=\min(X,Y)$ and for $W=\max(X,Y)$
4 votes
2 answers
373 views

What is the density of the $m$'th element of a sorted vector of $n$ uniformly distributed random variables

$X_1, X_2, ..., X_n$ are independent and uniformly distributed on $[0, 1]$. Sorting them yields a vector, whose first and last element have densities that are just the derivatives of products of CDFs. ...