Question 46
The Cantor set is defined as the set of real numbers $x$ such that $0 \leq x \lt 1$ and the digit $1$ does not appear in the base-$3$ expansion of $x$. Two numbers are uniformly and independently selected at random from the Cantor set. Compute the expected value of their absolute difference.
(Formally, one can pick a number $x$ uniformly at random from the Cantor set by first picking a real number $y$ uniformly at random from the interval $[0,1)$, writing it out in binary, reading its digits as if they were in base-$3$, and setting $x$ to $2$ times the result.)
(Formally, one can pick a number $x$ uniformly at random from the Cantor set by first picking a real number $y$ uniformly at random from the interval $[0,1)$, writing it out in binary, reading its digits as if they were in base-$3$, and setting $x$ to $2$ times the result.)