----- Original Message -----
From: Bob Parks <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Thursday, March 30, 2000 6:44 AM
Subject: testing a coin flipper
> Consider the following problem (which has a real world
> problem behind it)
>
> You have 100 coins, each of which has a different
> probability of heads (assume that you know that
> probability or worse can estimate it).
>
> Each coin is labeled. You ask one person (or machine
> if you will) to flip each coin a different number of times,
> and you record the number of heads.
............................................................................
..........................
Incidentally, I found that William Feller in chapter III (vol I) of his
classic book "An Introduction to Probability Theory and its Applications",
covers coin flipping nicely.
The sequence is treated as a random walk. The probability of the sign
reversal (i.e. heads is +1 and tails is -1) is low, indicating long
intervals between successive crossing of the axis. His Theorem 1 (page 84)
states that the probability (e), that up to epoch 2n+1 (n flips), there
occurs exactly r changes of sign equals 2 times the probability of the sum
of events being equal to 2r+1 in 2n+1 trials. (Involves the number of paths
to 2r+1 out of 2n+1 trials.)
His table on page 85 gives the probabilities of zero sign reversal in 99
trials as 0.1592, which is surprisingly high.
DAHeiser
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===========================================================================
