This question is being posed again because some people have more arguments to make with this one.
Two positive reals are selected at random from 0 to infinity. Let A be the smaller of the two, B the larger. What's the expected value for A/B?
Given a set of values x, with each value having a probability p of occurring, such that ∑p = 1. Then the expected value is ∑xp. For example, the expected value for a typical thrown 6-sided dice is
(1)(1/6)+(2)(1/6)+(3)(1/6)+(4)... = 7/2. = 3.5
It doesn't work to first work this out for 0 < A,B < N for some finite N, and then let N -> ∞, because that introduces a sampling bias.
The answer that i had posted is the definite integral of Tan((π/4)x) between 0 < x < 1, which yields the value 0.441271 approximately.
2007-04-06
13:14:02
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7 answers
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asked by
Scythian1950
7
in
Mathematics