A permutation of the distinct values `1` through `100` is revealed from left to right. Replace the current maximum whenever the revealed value is strictly greater than every earlier value. 1. What is the expected number of replacements? 2. Repeat the calculation when the shuffled multiset is `1, 2, ..., 98, 100, 100`, where a second copy equal to the current maximum does not count as a replacement. ### Constraints & Assumptions - Every ordering of the distinct list is equally likely. - For the multiset, start from a uniformly random permutation of labeled copies and then ignore the labels on the two `100` values. - The first revealed value counts as a replacement. ```hint Use indicator variables For each value, ask whether it appears before every strictly larger value. ``` ### What a Strong Answer Covers - Linearity of expectation without requiring record events to be independent. - The harmonic-number result for distinct values. - Correct treatment of the duplicated maximum and strict comparison in the follow-up. ### Follow-up Questions - What is the asymptotic growth of the expectation? - How would a replace-on-greater-or-equal rule change the duplicate case? - What is the probability of exactly one replacement in the distinct case?