Natural numbers permutation

Discrete Mathematics Level 5

The numbers 1,2,...,101 are randomly permuted. Define a number to be a local maxima if it is larger than it's 2 neighbouring numbers.

i.e. 5 and 7 are local maxima in the sequence 5,4,7, 6.

What is the expected number of local maxima in the permuted sequence.

NOTE: This problem is not original.


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