Paradoxes of Probability and Other Statistical Strangeness
1–10 of 93 posts
Re: Paradoxes of Probability and Other Statistical Strangeness
#2"Paradox" is a pretty strong term. The items presented are more in the category of common errors and counter-intuitiveness.
Re: Paradoxes of Probability and Other Statistical Strangeness
#3Another "paradox": even though it's possible to randomly pick a rational number from the reals, the probability of this happening is 0.
Re: Paradoxes of Probability and Other Statistical Strangeness
#4Another "paradox": even though it's possible to randomly pick a rational number from the reals, the probability of this happening is 0.
Please describe how it is possible to pick such a number. For example, I can readily imagine how to pick a random 32b float, but that it is an entirely problem with a nonzero probability.
Re: Paradoxes of Probability and Other Statistical Strangeness
#5Another "paradox": even though it's possible to randomly pick a rational number from the reals, the probability of this happening is 0.
Please describe how it is possible to pick such a number. For example, I can readily imagine how to pick a random 32b float, but that it is an entirely problem with a nonzero probability.
*entirely different
Re: Paradoxes of Probability and Other Statistical Strangeness
#6Another "paradox": even though it's possible to randomly pick a rational number from the reals, the probability of this happening is 0.
Please describe how it is possible to pick such a number. For example, I can readily imagine how to pick a random 32b float, but that it is an entirely problem with a nonzero probability.
Usually in math we assume the axiom of choice :) https://en.wikipedia.org/wiki/Axiom_of_choice I'm assuming this could somehow lead to such a "random" pick in the technical sense.
In terms of implementation, I'm not aware of an algorithm that can randomly pick a real number on an actual computer. Perhaps a mathematician could show how to pick one on some abstract machine with infinite resources, and not constrained by finite bit representations of numbers.
Re: Paradoxes of Probability and Other Statistical Strangeness
#7Another "paradox": even though it's possible to randomly pick a rational number from the reals, the probability of this happening is 0.
Please describe how it is possible to pick such a number. For example, I can readily imagine how to pick a random 32b float, but that it is an entirely problem with a nonzero probability.
In probability theory, when dealing with continuous sample spaces / random variables, events with probability 0 still have a chance of occurring, and events with probability 1 stil l have a chance of NOT occurring, see:
https://en.wikipedia.org/wiki/Almost_surely
This strange property comes from strange properties of the real numbers (and uncountably infinite sets) that give rise to things like:
https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
Measure theory deals with resolving this:
Re: Paradoxes of Probability and Other Statistical Strangeness
#8Re: Paradoxes of Probability and Other Statistical Strangeness
#9Another "paradox": even though it's possible to randomly pick a rational number from the reals, the probability of this happening is 0.
There is no uniform probability distribution on the reals.
Perhaps you meant the interval from 0 to 1?
Re: Paradoxes of Probability and Other Statistical Strangeness
#10Another "paradox": even though it's possible to randomly pick a rational number from the reals, the probability of this happening is 0.
there are a number of similar paradoxes that arise when considering infinities of different sizes!
Infinity Paradoxes - Numberphile - https://www.youtube.com/watch?v=dDl7g_2x74Q