473.Local Maxima in a Random Line-Up
★★★expected valueCh. 6 — Random Variables and Expectation444+ Problems in Probability
Fourteen papers labelled 1–14 are arranged in a line uniformly at random. Position is a local maximum if its paper is strictly larger than the papers adjacent to it (positions at the ends have only one neighbor). Find the expected number of local maxima.
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Ends need to beat 1 neighbor, interior spots must beat 2. Linearity over the 14 positions.
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