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
November 22, 2003 6:07 PM
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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