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This document provides solutions to 3 problems about geometric distributions, matchings in graphs, and the relationship between matchings and vertex covers. Problem 1 calculates the expectation of a geometric random variable X with parameter p to be 1/p. Problem 2 proves that a perfect matching exists in a bipartite graph modeling a chessboard with pieces in each row and column, allowing 8 non-attacking pieces to be selected. Problem 3 establishes that the size of a maximum matching is less than or equal

Author

Chenyang Fang

Language

EN