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Politics : Formerly About Advanced Micro Devices -- Ignore unavailable to you. Want to Upgrade?

To: jcholewa who wrote (128025)	11/10/2000 2:05:24 PM
From: pgerassi	Read Replies (2) \| Respond to of 1570958

Dear JC: Perhaps you should look at your statistics book again. The actual probability of 500 tails in 2,000 tosses is 500!*1500!/2000! far more than 1 in 2^2000. 1 in 2^2000 is for the chance that the first 500 tosses are tails and the last 1500 tosses are heads, or simply any single sequence of 2000 results. The best way is to use the standard deviation of coin tosses when tosses are large which (I think (no text handy)) is (n^.5)/2. With n = 2000, stddev is 22.4. The result is 500 tosses from the mean or 22.4 times stddev. The result being at least 500 away toward either side is about e^(-22.4) or about 1 in a billion shot (in my head estimate). Since you want one direction only, divide by 2. So it's a 1 in 2 billion shot which is far above the chances you stated. This however has nothing to do with the actual numbers above. Any time humans get involved, the randomness goes away and the results are not independent as required by these ideal situations. In communications, error bursts are far more likely than the above would state. It is not uncommon for a detector to error 1000 bits in a row all one way. Thus in communications, having 1000 more zeros than ones is not all that unlikely (even more so with humans in the loop). Remember errors are not random if, independence between results is not assured. Answer this Scumbria, why are some counties exactly the same after a recount? BTW, hand tabulation is much more error prone than machine tabulation due to the probability of much more human error. Pete