Re: Expected value

In article <4320866B.4020907@xxxxxxxxxxxx>,
Stephen J. Herschkorn <sjherschko@xxxxxxxxxxxx> wrote:

>Actually, a better approximation would be 303.5/3.5 = 86.714. This
>follows from the fact the final sum is approximately uniformly
>distributed on {301, 302,..., 306}. In fact, if we let the goal (300 in
>the original problem) grow arbitrarily large, the limiting distribution
>of the overshoot is discrete uniform.

Nonsense. A final sum of 306 can only happen in one way: hit 300 and
then roll a 6. A final sum of 301 can happen if you hit 295 and roll 6,
or hit 296 and roll 5, or ... So the final sum is about 6 times as
likely to be 301 as 306. An exact calculation shows the probability
of ending with 300+k is within 1.8*10^(-42) of (7-k)/21 for k = 1 to 6.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada



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