The heads-minus-tails distribution is the statistical distribution of 
, the absolute difference
between the numbers of heads and tails in 
independent tosses of a fair coin,
where 
is a positive integer. It is given by
 |
(1)
|
with probability zero at every other value. The most probable value is 
for 
, while 
and 
are tied for 
. The expectation value
is
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
The generating function for 
is given by
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(6)
|
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(7)
|
(OEIS A001803 and A046161) for 
(Prévost 1933, Abramowitz and Stegun 1972, Hughes 1995). These numbers also
arise in one-dimensional random walks.
