Answer by Kenneth Schilling for What are two independent, uniformly...
Let's not be so technical. Choose a number x in [0,1] whose decimal representation is .x_1x_2x_3x_4... . Then the random variables y=x_1x_3x_5... and z=x_2x_4x_6... are independent and uniformly...
View ArticleAnswer by Yuri Bakhtin for What are two independent, uniformly distributed...
Using binary digits of a uniformly distributed random variable on [0,1] is the first step in obtaining a variety of distributions in various spaces.In fact, distributions on almost any reasonable...
View ArticleAnswer by Pietro Majer for What are two independent, uniformly distributed...
Let us consider more closely the question about space-filling curves. The Peano curve and the Hilbert curve, and several other variations of them, have parametrizations $[0,1]\to[0,1]^2$ that actually...
View ArticleAnswer by Will Sawin for What are two independent, uniformly distributed...
There's no particular reason to use a continuous space-filling curve, other than style points. Just expand x in binary and send the odd digits to $f$ and the even digits to $g$. To prove that you get...
View ArticleWhat are two independent, uniformly distributed random variables on the unit...
I have been dabbling in learning basic things about probability theory and (of course) being of the school of abstract nonsense I have tried to understand things in its language. I apologize if this...
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