For a specific query Q, suppose that a search engine can produce up to 3 results, where the i-th result has probability 1/(2i) of being relevant. That is, 1st result has probability 1/2, 2nd has 1/4, 3rd has 1/6, and so on. Also, assume Q has a total of 3 relevant results in the collection.
C1: What is the expected average precision (AP) if the engine outputs 2 results?
C2: How many results should the search engine output to maximize the expected AP? Show your calculations and results.
C3: How many results should the search engine output to maximize F (harmonic mean of precision and recall)? Show your calculations and results.