# 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 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?
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Let X represent the difference between the number of heads and the number of tail obtained when a coin is tossed n times.
We are interested in all possible outcomes of X.
In n coins tossed tails can be obtained 0,1,2,……….,n times. If tails are obtained k times number of heads or obtained precisely n-k times.
Therefore, let us t be the number of tails and h=n-t number of heads. Lets define
$X=h-t=n-t-t=n-2t$
Therefore all possible outcomes of X can be described by
$\left\{n-2t|t=\left\{0,1\dots ..,n\right\}\right\}$.
Thus, we done.
Result:
Possible values of X are $n-2t|t=0,1\dots ..,n$.