BM$25$ is a measure of how relevant a document is for a query. Below is the formula for Okapi

BM$25$:

RSV

BM $25$

$=$ log

N

df

i$$q i

$\backslash$times

$($k$1$

$+1)$tf

i

k$1$

$((1-$ b$)+$ b

dl

avdl

$)+$tf

i

$($i$)$ Show how BM$25$ performs on the query $$employee benefits$.$ Below are some statistics

for our corpus.

Number of webpages $1000$

Number of webpages containing $$employee$10$

Number of webpages containing $$benefits$100$

Average document length $78$

There are only two documents relevant to $$employee benefits$.$ Below are their statistics

Document #$1$ Document #$2$

Document length $2639$

Frequency of $$employee$34$

Frequency of $$benefits$32$

Let k$1=1$ and b $=0\mathrm{.}6.$