1 .
You repeatedly, and independently, flip three fair coins, until there are exactly two heads among
the three flips. Define the random variable $X$ to be the total number of coin flips.
For example, if the coin flips result in
$$
(TTT), (THT), (HHH), (HTH),
$$
then $X = 12$.
What is the expected value $\mathbb{E}(X)$ of $X$?
What is the expected value $\mathbb{E}(X)$ of $X$?
(a)
8
(b)
3/8
(c)
12
(d)
8/3