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Forum: Probability 12-21-2005, 08:00 AM
Replies: 21
Views: 16
Posted By irchans
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,...
Forum: Probability 11-08-2005, 05:45 PM
Replies: 9
Views: 9
Posted By irchans
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
Forum: Probability 10-23-2005, 02:46 PM
Replies: 31
Views: 16
Posted By irchans
Lowest Integer : Game Theory

Did anyone ever figure out the game theoretic solution for N players?
Forum: Probability 09-20-2005, 06:02 PM
Replies: 5
Views: 11
Posted By irchans
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...
Forum: Probability 09-10-2005, 09:02 AM
Replies: 4
Views: 8
Posted By irchans
Forum: Probability 09-10-2005, 09:00 AM
Replies: 44
Views: 16
Posted By irchans
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...
Forum: Probability 08-28-2005, 02:41 PM
Replies: 15
Views: 11
Posted By irchans
Theory: 11.7447%, Excel Simulation: 10.4%, Mathematica Sim 11.3%

I agree, there are 901 windows. That changes the theoretical answer to 11.7447%.

For the Excel simulation, I agree that cell E1 should be =D1. In the other E cells I had max of cells D(i-1) and...
Forum: Probability 08-27-2005, 10:00 PM
Replies: 15
Views: 11
Posted By irchans
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...
Forum: Probability 08-27-2005, 12:16 PM
Replies: 15
Views: 11
Posted By irchans
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...
Forum: Probability 08-27-2005, 09:39 AM
Replies: 15
Views: 11
Posted By irchans
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...
Forum: Probability 08-05-2005, 10:48 PM
Replies: 15
Views: 12
Posted By irchans
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...
Forum: Probability 08-05-2005, 09:22 PM
Replies: 15
Views: 12
Posted By irchans
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:...
Forum: Probability 08-05-2005, 04:36 PM
Replies: 15
Views: 12
Posted By irchans
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...
Forum: Probability 08-05-2005, 07:28 AM
Replies: 15
Views: 12
Posted By irchans
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...
Forum: Probability 08-03-2005, 07:03 PM
Replies: 12
Views: 12
Posted By irchans
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...
Forum: Probability 07-26-2005, 07:10 AM
Replies: 37
Views: 16
Posted By irchans
Re: Two New Variations

Lovely solution. I didn't sit down to figure it out before reading your post. I should have!
Forum: Probability 07-25-2005, 09:27 PM
Replies: 37
Views: 16
Posted By irchans
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...
Forum: Probability 07-25-2005, 09:16 PM
Replies: 37
Views: 16
Posted By irchans
Re: A birthday puzzle

Very Nice Ken.
Forum: Probability 07-25-2005, 09:11 PM
Replies: 37
Views: 16
Posted By irchans
LetYouDown, can you post your code? (NM)

Maybe we can find the flaw.
Forum: Probability 07-25-2005, 08:49 PM
Replies: 15
Views: 12
Posted By irchans
Re: Another theatre line problem

Cute. My answer is below in white

<font color="white"> 2.93 on average </font>
Forum: Probability 07-16-2005, 11:20 AM
Replies: 14
Views: 11
Posted By irchans
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...
Forum: Probability 07-16-2005, 10:02 AM
Replies: 4
Views: 9
Posted By irchans
Re: Probability of one OR more person getting dealt hands XX-YY

vqchuang,

The correct answer is somewhat complicated but here is an approximation:

if

X=number of hands that call me (it would be something out of 1225)
Y=number of players still to...
Forum: Probability 07-16-2005, 09:52 AM
Replies: 7
Views: 9
Posted By irchans
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...
Forum: Probability 07-15-2005, 06:56 AM
Replies: 14
Views: 11
Posted By irchans
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.
Forum: Probability 06-15-2005, 08:01 AM
Replies: 26
Views: 14
Posted By irchans
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.
Showing results 1 to 25 of 217

 
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