Chapter 15.5, Problem 11P

Show that the expected number of heads in a single toss of a coin is $\frac{1}{2}.$ Show in two ways that the expected number of heads in two tosses of a coin is 1:

(a) Let $x=$ number of heads in two tosses and find $\bar{x}$

(b) Let $x=$ number of heads in toss 1 and $y=$ number of heads in toss 2; find the average of $x+y$ by Problem 9. Use this method to show that the expected number of heads in $n$ tosses of a coin is $\frac{1}{2}n.$