| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
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From: [email protected] (Sir Six)
Newsgroups: sci.math
Subject: Impressive Coin Flips
Message-ID: <[email protected]>
Date: 3 Mar 90 05:03:39 GMT
Sender: [email protected]
Organization: University of California, San Diego
Lines: 45
Suppose we have a coin, weighted to give heads with a probability p.
We flip it f times, and get h heads. We define P as the probability
of getting h heads in f flips:
h f-h f!
P(p,h,f) = p (1-p) --------
f!(f-h)!
Furthermore, we define the "impressiveness" of <H,F> to be the
probability of flipping fewer than H heads with F flips, for a coin
weighted to give heads with probability p:
H-1
I (H,F) = SUM P(p,h,F)
p h=0
I (0,F) = 0 for all F, p.
p
Now, with two sets of flips, <H1,F1> and <H2,F2>, we want to
determine which is "more impressive." Unfortunately, we don't know
the weight of the coin, so p is an unknown. Suppose we define
1 /H1 H2\
p = - * | -- + -- |
2 \F1 F2/
Then we define the "More impressive" operator:
MI(<H1,F1>,<H2,F2>) is true iff I (H1,F1) > I (H2,F2) with p defined
as above. p p
We can define "Less impressive" and "as impressive" operators
similarly. Now, to the question:
I want to know whether MI is transitive: I.e., if
MI(<H1,F1>,<H2,F2>) and MI(<H2,F2>,<H3,F3>), does it follow that
MI(<H1,F1>,<H3,F3>)?
Don't ask me where I come up with these. I wish I knew.
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1201.1 | 4GL::GILBERT | Ownership Obligates | Tue Mar 06 1990 13:12 | 1 | |
I'm pretty sure it's not transitive. Now to find a counterexample.... | |||||
| 1201.2 | not transitive | 4GL::GILBERT | Ownership Obligates | Tue Mar 06 1990 17:40 | 11 |
> I want to know whether MI is transitive: I.e., if > MI(<H1,F1>,<H2,F2>) and MI(<H2,F2>,<H3,F3>), does it follow that > MI(<H1,F1>,<H3,F3>)? No. Example: MI(<11,19>,< 7,12>) MI(< 7,12>,< 2, 3>) MI(< 2, 3>,<11,19>) (Dan, could you send this counterexample back to the poser? Thanks.) | |||||