Assume 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.