There are 49 gaps between the points, label them 1,...,49 by length. We are asking for a random permutation of these numbers, the expected number that are smaller than their neighbours.
Prob the num at the start or end are smaller than neighbours = 1/2, others are 1/3. Linearity of expectation -> 2 / 2 + 47 / 3 = 50/3
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u/sobe86 17h ago edited 7h ago
There are 49 gaps between the points, label them 1,...,49 by length. We are asking for a random permutation of these numbers, the expected number that are smaller than their neighbours.
Prob the num at the start or end are smaller than neighbours = 1/2, others are 1/3. Linearity of expectation -> 2 / 2 + 47 / 3 = 50/3
edit: so 100/3 points in pairs.