info prev up next book cdrom email home

Heads Minus Tails Distribution

A fair Coin is tossed $2n$ times. Let $D\equiv\vert H-T\vert$ be the absolute difference in the number of heads and tails obtained. Then the probability distribution is given by

({\textstyle{1\over 2}})^{2n}{2n\choose n} ...
...xtstyle{1\over 2}})^{2n}{2n\choose n+k} & $k=1$, 2, \dots,\cr}

where $P(D=2k-1)=0$. The most probable value of $D$ is $D=2$, and the expectation value is

\left\langle{D}\right\rangle{}={n{2n\choose n}\over 2^{2n-1}}.

See also Bernoulli Distribution, Coin, Coin Tossing


Handelsman, M. B. Solution to Problem 436, ``Distributing `Heads' Minus `Tails.''' College Math. J. 22, 444-446, 1991.

© 1996-9 Eric W. Weisstein