3. Let W = 2<sup>N</sup>, where N ~ Geometric(p). In class, we showed that when p = 1/2,
E(W) = ?. For all the other values 0 < p < 1 p ? 1/2, find* E(W). When is it
finite?
*For #3, you may need the following fact from calculus: if 0 < r < 1, $\sum_{k=0}^{\infty} r^k = 1 + r + r^2 + ... = \frac{1}{1 - r}$.
If r ? 1, then 1 + r + r<sup>2</sup> + ... = ?.
