Question $2(80$ points$)$

Consider the following one$-$hot vector matrix for five books $($Book$1,$ Book$2,$ Book$3,$ Book$4,$ Book$5)$:

$\backslash$table$[[,$Fiction,Mystery,Romance,Science,Biography$],[$Book$1,0,1,1,0,0],[$Book$2,0,1,0,1,0],[$Book$3,1,1,0,0,0],[$Book$4,0,0,1,1,0],[$Book$5,0,0,1,0,1]]$

Answer the following FIVE questions:

a$.$ Suppose a user A likes Book$2$ and Book$3,$ rank Book$1,$ Book$4,$ and Book$5$ according to the predicted preferences for them. $(15$ points$)$

b$.$ Suppose a user B likes Book$4$ and Book$5,$ rank Book$1,$ Book$2,$ and Book $3$ according to the predicted preferences for them. $(15$ points$)$

c$.$ Suppose a user C gave ratings to Book$1,$ Book$2,$ and Book$4$ respectively as $4,3,2($min $1$ and max $5),$ rank Book$3$ and Book $5$ with an unweighted user profile. $(15$ points$)$

d$.$ For the same user C of Question c$,$ rank Book$3$ and Book$5$ with a weighted user profile. $(15$ points$)$

e$.$ Suppose a user D likes Book$1,$ Book$2,$ and Book$3,$ but dislikes Book$4$ and Book$5,$ select a method among the Probabilistic Method, Linear Regression, and Decision Tree, to predict whether she likes Book$6$ that belongs to Science and Biography. $(20$ points$)$