Peaks in a Permutation
The numbers 1, 2, ..., 10 are placed in a row in uniformly random order. A position is a peak if its number is larger than the number in each adjacent position. The two end positions have only one neighbour, so an end position is a peak if it exceeds that single neighbour. What is the expected number of peaks? Give a reduced fraction (a decimal rounded to two places is also accepted).
Related problems & prerequisites
Worth solving first
- Expected Disorder 2.0/10
- Like Next to Like 2.0/10
- Monochromatic Triangles 2.0/10
Source: Standard indicator-variable exercise on permutations; no single originator. Statement written for AxiomIQ.