answer after part f i mean g$,$h$,$i$,$j$,$k$,$i$,$ii$,$iii$($f$)$ Provide an example ranking for this query that maximizes $R$@$10[5$ points$]$

$($g$)$ You have reason to believe that the users of this system will want to examine every

relevant document for a given query. In other words, you have reason to believe that

users want perfect recall. You want to evaluate based on $P$@$K.$ Is there a query$-$specific

method for setting the value of $K$ that would be particularly appropriate in this scenario?

What is it$?$ Your answer should be related to R$-$Precision. $[10$ points$]$

$($h$)$ Compute average precision $($AP$).[10$ points$]$

$($i$)$ Provide an example ranking for this query that maximizes average precision $($AP$).[5$

points$]$

$($j$)$ Compute DCG$5($i$.$e$.,$ the discounted cumulative gain at rank $5).[10$ points$]$

$($k$)$ NDCG$5$ is given by NDCG$5=$ DCG$5/$IDCG$5,$ where IDCG$5$ is the DCG$5$

associated with the ideal top$-5$ ranking associated with this query. $[10$ points$]$

$($i$)$ What is the ideal top$-5$ ranking associated with this query $($notice that the query has $1$

perfect document, $1$ excellent document, $3$ good documents, $2$ fair documents, and the

rest of the documents are bad$)?[10$ points$]$

$($ii$)$ IDCG$5$ is the DCG$5$ associated with the ideal ranking. Compute IDCG$5.($Hint:

compute DCG$5$ for your ranking proposed in part $($i$).)[10$ points$]$

$($iii$)$ Compute NDCG$5$ using the formula above. $2$: Precision$-$Recall Curves $[15$ points$]$

A Precision$-$Recall $($PR$)$ curve expresses precision as a function of recall. Usually, a PR$-$

curve is computed for each query in the evaluation set and then averaged. For simplicity,

the goal in this question is to draw a PR$-$curve for a single query. Draw the PR$-$curve

associated with the ranking above $($same query, same results$).$ Hint: Your PR curve

should always go down with increasing levels of recall $($interpolation$).[20$ points$]$