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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
1
vote
How much reduction in expected variance can we get from a single bit?
This is a specific instance of one-shot lossy source coding which is still open in general. The best work I know of is in this preprint by Elkayam and Feder where they distill it down to the open prob …
0
votes
Transforming random variables for having good property?
No, of course not.
You cannot generally get $X,Y$ to surely satisfy your desired typical events $\Omega$ and $\Lambda$ by transforming them individually. Let alone finding a somehow negligibly-distor …