Chapter 12.5, Problem 18E

(a)

To determine

The probability that exactly $n$ consecutive tails occur when a fair coin is tossed until a head appears.

(b)

To determine

The average number of consecutive tails that occur when a fair coin is tossed until a head appears.

(c)

To determine

The infinite series that gives the variance for the number of consecutive tails and show that the variance equals $2$.