Enuma Elish
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I 'm not sure the formula is right.
If it's three random variables are you sure that:
f1.(1-erf2).(1-erf3)+ f2.(1-erf1).(1-erf3)+ f3.(1-erf1).(1-erf2)
integrates to 1 ?
But see this:
http://www.itl.nist.gov/div898/handbook/apr/section1/apr181.htm
I 'm following your reasoning.
"A" can cross the finish line at any time 0 to infinity.
Practically, with a mean of 57.00 secs it can be 55.00 seconds (a record performence) to infinite (goes lame - stops !). In our ideal model where lameness-jockey accidents do not exist, for all intends and...
PROB(A) = \int dt . fa(t) \prod(1-erf(\mu,\sigma,t))
That does n't look great but I think this is it.
The integral is from 0 to infinity.
fa is the Gaussian of "horse A".
erf are the cdfs of the Gaussians of B-C-D-E-F.
Simlilarly for the others.
It's a hell of an integral though.
How...
integrals
EnumaElish imports some good looking math symbols.
Can one get those from the font menu ?
Anyway is it
P(A) = integral from 0 to infinity of {erf(t,Mb,Sb) x erf(t,Mc,Sc) ... x erf(t,Mf,Sf)} ?
What is the distribution of t(min/A) then ?
Simulation gives the following results for the numbers in my example:
horse 1: 0.47
horse 2: 0.29
horse 3: 0.19
horse 4: 0.04
horse 5: 0.01
horse 6: 0.00
(plus-minus 0.01)
A horse race is going to take place with six runners.
The race is over 5 furlongs (1000 meters) and for each of the six contestants it is known that their probable times at this distance are:
horse 1: 57.00 sec
horse 2: 57.20 sec
horse 3: 57.35 sec
horse 4: 57.80 sec
horse 5: 58.10 sec...
Hello
This is a question from the recent national exams in Physics in Greece:
Two equal sized coins (1 euro) are placed on one edge of a frictionless flat table.
Coin "A" has a continuous force F applied at it's centre and pointing to the opposite edge of the table. Coin "A", as a result...