Task $2$: Design a Jelinek$-$Mercer based Language Model $($JM$\_$LM$)$ that ranks documents in

each data collection using the corresponding topic $($query$)$ for all $50$ data collections.

Inputs: $50$ long queries $($topics$)$ in the$50$Queries.txt and the corresponding $50$ data collections

$($Data$\_$C$101,$ Data$\_$C$102,...,$ Data$\_$C$150).$

Output: $50$ ranked document files $($e$.$g$.,$ for Query R$107,$ the output file name is

$$JM$\_$LM$\_$R$107$Ranking.dat$)$ for all $50$ data collections and save them in the folder

$$RankingOutputs$.$

For each long query $($topic$)$ Rx$,$ you need to use the following equation to calculate a conditional

probability for each document D in the corresponding data collection $($dataset$)$:

$3$

where is the number of times query word qi occurs in document D$,|$D$|$ is the number of

word occurrences in D$,$ is the number of times query word qi occurs in the data collection

Data$\_$Cx$,|$Data$\_$Cx$|$ is the total number of word occurrences in data collection Data$\_$Cx$,$ and

parameter $\backslash$lambda $=0\mathrm{.}4.$