Medium

Probability

$14$ pieces of paper labelled $1-14$ are placed in a line at random. We spot $i$ is a local maxima if the paper at the $i$th position is strictly larger than all of it's adjacent papers. Find the expected number of local maxima in the sequence. For example, with $6$ numbers, 513246 has $3$ local maxima at the first, third, and last spots.

Notes

Hint