$3\mathrm{.}5.$ Suppose that a data warehouse for Big University consists of the four dimensions student,

course, semester, and instructor, and two measures count and avg grade. At the lowest conceptual

level $($e$.$g$.,$ for a given student, course, semester, and instructor combination$),$ the avg grade measure

stores the actual course grade of the student. At higher conceptual levels, avg grade stores the

average grade for the given combination.

$($a$)$ Draw a snowflake schema diagram for the data warehouse.

$($b$)$ Starting with the base cuboid $[$student$,$ course, semester, instructor$],$ what specific OLAP

operations $($e$.$g$.,$ roll$-$up from semester to year$)$ should you perform in order to list the

average grade of CS courses for each Big University student.

$($c$)$ If each dimension has five levels $($including all$),$ such as $$student $<$ major $<$ status $<$ university

$<$ all$,$ how many cuboids will this cube contain $($including the base and apex cuboids$)?$