Solution: 2014 Winter Final - 24
Author: Michiel SmidQuestion
We flip a fair coin independently $n$ times. Define the random variable
- X = the number of heads minus the number of tails in the sequence of $n$ flips.
(a)
$n/8$
(b)
$0$
(c)
$n/4$
(d)
$n/2$
Solution
$ X = H - T $
- $E(H) = n \cdot \frac{1}{2} = \frac{n}{2}$
- $E(T) = n \cdot \frac{1}{2} = \frac{n}{2}$
We may use Linearity of Expectations on $E(X)$
$E(X) = E(H) - E(T) = \frac{n}{2} - \frac{n}{2} = 0$