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Runs in Bernoulli Trials

While attempting to work out the probability of Joe DiMaggio's hitting streak, I tumbled across this handy looking formula, in Ask Dr. Math.

The probability of no run of length r in n trials is approximately


  • q(n) = [(1-px)/(r+1-rx)q] * 1/x^(n+1)
  • x = 1 + q.p^r + (r+1)(q.p^r)^2 + ....

November 22, 2003 6:07 PM | TrackBack

Comments

Dear Dr.,

I am a doctoral candidate of Beijing University of Chemical Technology in China. I know about from your homepage about the theory of Bernoulli trials. I have one question and wnat to ask your help.

Asuming we have a 100 x 100 grids. The state for each grid is either "crystalline" or "amorphous". At time t=0, the status of all grids is assessed from consecutive Bernoulli trials. This yields a random distribution of "crystalline" or "amorphous" areas on the grid:

If probablity for "amorphous grid" is P, then
probablity for "crystalline grid" is 1-P.

where P is the crystallinity of the system. So here P is the probablity that a grid G(i, j) represents a "crystalline" or "amorphous" part (i=1, 100; j=1,100).

How od I arrange a state for each grid, i.e., How do I get a distribution of the states among these grids?

Thank you very much!

You would be appreciated if you could reply as possible as your earliest convenience.

best wishes,
Qingyuan Yang

Comment by: Qingyuan Yang July 29,2004
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