Simple probability question General forum
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5 replies. Last post: 2015-01-29
Reply to this topic Return to forumCould someone please explain me how it works for comparing uniform distributions?
I have three independent uniform distributions:
a from 0 to Ab from 0 to Bc from 0 to Cwith A<=B<=C
so why P(a is max(a,b,c)) is A^2/(6BC) and not P(a>b).P(a>c) ?( P(a>b) = A/2B )I know that for identical uniform distributions, the min, median and max tend to be evenly distributed in the interval at 1/4, 2/4, 3/4, each being in the middle of the space left when you have put the others.
what is the formula for P(a is min(a,b,c)) ?
This is not a school problem, I'm trying to solve analytically some [0,1] toy poker games…
Textile garbling again is really annoying.
a from 0 to A
b from 0 to B
c from 0 to C
with A<=B<=C
Anyone knows how to write in the forum without lines being aggregated?
shouldn't it be A^2/(3BC)? (if A=B=C, shouldn't it be 1/3?)
It's not P(a>b)P(a>c) because those a>b and a>c aren't independent events. Both are saying “a is big”, so why “a is big” should be uncorrelated with “a is big”?
Your probability space is a brick in 3D space. The part with b > A or c > A contributes nothing to the probability in question, so we're only interested in the cube 0 <= a, b, c <= A. This cube's volume is A/B * A/C of all the brick's volume. And the a=max() set occupies 1/3 of the cube due to symmetry. There, 1/3 * A/B * A/C = A^2/(3BC).
Oh thanks alihv for this geometrical explanation, it seems so simple now!
Yes you are right, A^2/(6BC) was half this volume with added condition that b>c, so probability(a>b>c).