Forum: Probability
12-21-2005, 08:00 AM
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Replies: 21
Views: 1,513
Re: Math Degrees and Careers
Undergrad: Physics, EE, Math, Aerospace Engr, Nuclear Engineering, Astrophysics, Meteorology.
Grad: Math, Physics, Control Systems, Elec Engr., Economics, Psychometrics, Operations Research,...
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Forum: Probability
11-08-2005, 05:45 PM
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Replies: 9
Views: 428
Re: Software to calculate integrals
If f[t] = (5*t)/16 - (15*Sin[2*t])/64 + (3*Sin[4*t])/64 - Sin[6*t]/192,
then f '[t] = (Sin[t])^6,
f[Pi/2] - f[0] = 5 * Pi / 32 ~= 0.490873852123405193509788028637
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Forum: Probability
10-23-2005, 02:46 PM
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Replies: 31
Views: 937
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Forum: Probability
09-20-2005, 06:02 PM
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Replies: 5
Views: 256
Re: Recurrence Relation to Closed Form
Given F(N) = F(N-1)*(2N-1)*(2N)/2 and F(0)=1 what is F?
First you might notice this recurrence relation has the form
F(N) = F(N-1) * G(N).
Any recurrence relation of this form has a...
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Forum: Probability
09-10-2005, 09:02 AM
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Replies: 4
Views: 349
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Forum: Probability
09-10-2005, 09:00 AM
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Replies: 44
Views: 496
Re: Anything that can happen will happen?
If there are 10,000,000 spins a day for 1 billion years, then we can expect 49 reds in a row once. Thus I think we can safely say that 60 reds in a row will never occur on this planet (on a fair...
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Forum: Probability
08-28-2005, 02:41 PM
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Replies: 15
Views: 827
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Forum: Probability
08-27-2005, 10:00 PM
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Replies: 15
Views: 827
Re: Exact answer 11.7327% ? (edited)
I fixed some typos in the post below
I think it's possible to use recurrence formulas like Bruce's formaulas to get the exact answer.
Look at the 1000 hands as 900 overlapping windows of width...
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Forum: Probability
08-27-2005, 12:16 PM
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Replies: 15
Views: 827
Exact answer 11.7327% ?
I think it's possible to use recurrence formulas like Bruce's formaulas to get the exact answer.
Look at the 1000 hands as 900 overlapping windows of width 100.
The Probability p[n] that the...
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Forum: Probability
08-27-2005, 09:39 AM
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Replies: 15
Views: 827
Simulation Results
I wrote two quick simulations. Here are the results for the probability that at some time in a sequence of 1000 hands, there exists a 100 hand window with 14 or more pocket pairs.
In the first...
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Forum: Probability
08-05-2005, 10:48 PM
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Replies: 15
Views: 710
Re: Simulation Results
[ QUOTE ]
Now, if I want to expand this to see about 3 simultaneous failures, it should be pretty simple, right?
When two machines fail simultaneously, the average length of overlap...
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Forum: Probability
08-05-2005, 09:22 PM
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Replies: 15
Views: 710
Simulation Results
pvn,
I wrote a quick simulation for an additional comparison. I don't think my Mathematica code is really readable, but it beats writing a longer c++ program. Here is the code and the results:...
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Forum: Probability
08-05-2005, 04:36 PM
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Replies: 15
Views: 710
Oops - correction
pvn,
You are correct! There was a typo in my previous post. Below is the corrected version substituting 3 hours for 6. The expected number of overlaps did not change when I made the...
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Forum: Probability
08-05-2005, 07:28 AM
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Replies: 15
Views: 710
Re: reliability (no poker content)
uuDevil,
I think your method underestimates the number of overlaps because it implies that failures start exactly on a three hour boundary.
Here is a second method for estimating the...
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Forum: Probability
08-03-2005, 07:03 PM
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Replies: 12
Views: 379
Why is the answer 2000 + a/b?
[ QUOTE ]
[ QUOTE ]
Followup: Suppose you add the numbers up until you get 1000. Roughly how many do you expect it to take?
[/ QUOTE ]
It's easy to see that the average is a bit more than...
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Forum: Probability
07-26-2005, 07:10 AM
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Replies: 37
Views: 840
Re: Two New Variations
Lovely solution. I didn't sit down to figure it out before reading your post. I should have!
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Forum: Probability
07-25-2005, 09:27 PM
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Replies: 37
Views: 840
Two New Variations
Variation 1 (fairly easy if you can do the orignial variation)
The manager of a movie theatre announces that a free ticket will be given to the first person in line whose birthday and birth hour...
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Forum: Probability
07-25-2005, 09:16 PM
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Replies: 37
Views: 840
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Forum: Probability
07-25-2005, 09:11 PM
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Replies: 37
Views: 840
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Forum: Probability
07-25-2005, 08:49 PM
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Replies: 15
Views: 488
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Forum: Probability
07-16-2005, 11:20 AM
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Replies: 14
Views: 523
Experiment
I taped together a few pennies until the number of side results was approximately equal to the number of heads or tails. At about 11 pennies,
#sides ~= #heads ~= #tails.
A penny has a...
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Forum: Probability
07-16-2005, 10:02 AM
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Replies: 4
Views: 583
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Forum: Probability
07-16-2005, 09:52 AM
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Replies: 7
Views: 325
Comparison to flipping a coin 26 times
I agree with emp1346's answer. I thought it might be interesting to compare this question to a similar coin toss probability question.
The probability of getting n red cards when drawing 2 n...
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Forum: Probability
07-15-2005, 06:56 AM
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Replies: 14
Views: 523
Re: Quick Rando Question : Fair Coin
I would think that you would want the potential energy of lying on an edge to equal the potential energy of lying on a face. If those energies were equal then,
thickness = diameter.
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Forum: Probability
06-15-2005, 08:01 AM
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Replies: 26
Views: 846
Re: Running It Twice
EV is still the same even if the cards are not shuffled. Let me think about it for a bit and try to come up with a proof.
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