Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times

# Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times

S
40 points

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible values of X?

Let X
SnakeOil

8.7k points

Let H be the number of heads occurring and T be the number of tails occurring, then we have that

$X = H - T$

suppose we have all heads n number of times then,

$X = H-T = n-0 = n$

now suppose we have all heads minus 1 tail (or n-1 heads and 1 tails) then,

$X = H - T = (n-1)-1 = n-2$

again suppose we have all heads minus 2 tails (or n-2) heads and *2 tails) then,

$X = H-T = (n-2)-2 = n-4$

proceeding in this manner we see the sample space is given by,

$X \in (n, n-2, n-4, \ldots , 4-n, 2-n, -n)$

or

$X \in n-2i \text{ for } i=0,1,\ldots,n$

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