\problemdata
{s01 ps10}
{random variable}

\begin{problem} Suppose that I choose a listing of the
numbers $1, 2, \ldots, n$ uniformly at random.  What is the expected
number of entries that are greater than all preceding entries?  For
example, in the listing 4, 2, 1, 5, 3, the numbers 4 and 5 are greater
than all preceding entries\footnote{This problem can be equivalently phrased as follows: There are n people whose heights are $1, 2, \ldots, n$. I choose a random permutation, and line them up accordingly. What is the expected number of people who can see what's going on in front of the line? We are assuming that a person can see if and only if all the people in front of him/her are shorter.}

\hint What's the probability that the first entry is greater than all the preceding entries? What about the second one? 

\end{problem}