QUESTION $2(30$ marks$)$

Consider the project with the following estimates for activity times and precedence relationships:

$\backslash$table$[[$Activity$,\backslash$table$[[$Optimistic$],[$Time$]],\backslash$table$[[$Most$],[$Likely Time$]],\backslash$table$[[$Pessimistic$],[$Time$]],\backslash$table$[[$Immediate$],[$Predecessor$($s$)]]],[$A$,3,4,5,-],[$B$,5,7,9,-],[$C$,2,3,10,$A$],[$D$,2,5,8,$B$],[$E$,1,7,7,$B$],[$F$,3,5,7,$C$,$ D$],[$G$,7,8,9,$D$,$ E$],[$H$,2,6,10,$F$]]$

$($a$)$ Calculate the expected time for each activity $(8$ marks$)$

$($b$)$ What is the expected duration of the project? $(10$ marks$)$

$($c$)$ What is the project variance? $(6$ marks$)$

$($d$)$ If the deadline of the project is $25$ days, what is the probability of finishing the project on time? $(6$ marks$)$