At a local university, the Student Commission on Programming and Entertainment $($SCOPE$)$ is preparing to host its first rock concert of the school year. To successfully produce this rock concert, SCOPE has listed the requisite activities and related information in the following table $($duration estimates measured in days$).$

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessor$($s$)],[-]],\backslash$table$[[$Optimistic$],[8]],\backslash$table$[[$Most$],[$Probable$],[10]],\backslash$table$[[$Pessimistic$],[15]]],[$A:$,\backslash$table$[[$Negotiate contract$],[$with selected$],[$musicians$]]],[$B:$,$Reserve site,$-,7,8,9],[$C:$,\backslash$table$[[$Manage travel$],[$logistics for music$],[$group$]],$A$,5,6,10],[$D:$,\backslash$table$[[$Screen & hire$],[$security personnel$]],$B$,3,3,3],[E$:$,\backslash$table$[[$Arrange advertising$],[$& ticketing$]],B,C,1,5,9],[$F:$,$Hire parking staff,$D,4,7,10],[,\backslash$table$[[$Arrange concession$],[$sales$]],$E$,3,8,10]]$

a$.$ Draw the project network.

b$.$ Compute the expected duration and variance of each activity.

c$.$ Determine the critical path in the project network.

d$.$ What is the expected duration and variance of the critical path?