ssume that a search engine returns a ranked list of $10$ total documents for a given query. According to the ground truth labeling, there are $6$ relevant documents for this query $($assuming binary relevance$),$ and that the relevant documents in the ranked list are in the $1$st$,3$rd$,4$th$,7$th$,$ and $9$th positions in the ranked results.

$1.$ Calculate Precision, Recall, F$-$measure, nDCG$,$ at the $10$ retrieved documents.

$2.$ Calculate the Average Precision