b$)$ Calculate the Expected Time, the Earliest Expected Completion time $($TE$),$ the Latest Expected Completion Time $($TL$)$ and the Slack Time. Show critical path. Fill in the answer in Table $2.$

$\backslash$table$[[\backslash$table$[[$Activity$],[$No$.]],$ET$,T_E,T_L,$Slack time,Critical path$],[$A$,,,,,],[$B$,,,,,],[$C$,,,,,],[$D$,,,,,],[$E$,,,,,],[$F$,,,,,]]$

A project has been defined to contain the following list of activities along with their required times for completion.

Table $1$

$\backslash$table$[[\backslash$table$[[$Activity$],[$No$.]],$Activity,$\backslash$table$[[$Immediate$],[$Predecessors$]],\backslash$table$[[$Optimisti$],[$C Time$]],\backslash$table$[[$Pessimistic$],[$Time$]],\backslash$table$[[$Realistic$],[$Time$]]],[$A$,$Collect requirement,$-,4,8,6],[$B$,$Analyze process,A$,7,11,9],[$C$,$Design processes,A$,3,7,5],[$D$,$Design screen,A$,9,13,11],[$E$,$Test and document,B$,6,10,8],[$F$,$Install,C$,$ D$,$ E$,3,9,6]]$

Based on the Table $1,$

a$)$ Construct a Pert chart for the activities above.

b$)$ Calculate the Expected Time, the Earliest Expected Completion time $($TE$),$ the Latest Expected Completion Time $($TL$)$ and the Slack Time. Show critical path. Fill in the answer in Table $2.$

$\backslash$table$[[\backslash$table$[[$Activity$],[$No$.]],$ET$,T_E,T_L,$Slack time,Critical path$],[$A$,,,,,],[$B$,,,,,],[$C$,,,,,],[$D$,,,,,],[$E$,,,,,],[$F$,,,,,]]$