Probabilistic retrieval model: $($a$)$ Given a query as shown in the table, if we have the following document$-$term matrix and the associated relevance information for a probabilistic retrieval model. An entry $\text{'}1\text{'}$ indicates that the term occurs in a document, and $\text{'}0\text{'}$ means it does not: R or NR indicate the relevance of the document with respect to queries in the training data Assume the information retrieval system received two new documents and their vectors according to T $1$ through T $6$ are as follows: Probabilistic retrieval model:

$($a$)$ Given a query as shown in the table, if we have the following document$-$term matrix and the associated relevance information for a probabilistic retrieval model. An entry $\text{'}1\text{'}$ indicates that the term occurs in a document, and $\text{'}0\text{'}$ means it does not: R or NR indicate the relevance of the document with respect to queries in the training data

$\backslash$table$[[,$T$1,$T$2,$T$3,$T$4,$T$5,$T$6,$Relevance$],[$doc$1,1,0,1,1,0,0,R$

$[$ doc$11=(0,1,1,0,0,1)$; doc$12=(1,0,1,1,0,1)]$

Compute their retrieval status values $($RSV$)$ to find which one should be ranked higher $($note: please smooth the counting by adding $0\mathrm{.}5$ as shown in the following table$)$