Number of Records?

Suppose there are $n$ distinct numbers $x_1,\ldots, x_n$, and $y_1, \ldots, y_n$ is a random permutations of them. If $\exists k$ such that $y_k<y_i, \forall 1\le i<k$, then we say that $y_k$ is a record (we always count $y_1$ as a record). What is the expected number of records in $y_1, \ldots, y_n$?

See my neat solution here.