A partially solved PERT problem is detailed in the table below. Times are given in weeks. ActivityPrecedingTimeA$--9\mathrm{.}5$BA$3$CA$12$DA$5\mathrm{.}5$EB$6$FB$8$GC$,$ F$3$HD$3$IH$9$JG$,$ I$7$KE$,$ J$2\mathrm{.}5$ ActivityPrecedingOptimisticTimeProbableTimePessimisticTimeExpectedTimeVarianceA$--79141\mathrm{.}361$BA$2280$CA$812160$DA$35101\mathrm{.}361$EB$4680$FB$68100$GC$,$ F$2340$HD$2281\mathrm{.}000$IH$68162\mathrm{.}778$JG$,$ I$46142\mathrm{.}778$KE$,$ J$2250\mathrm{.}250$ a$.$ Draw the network diagram. b$.$ Calculate the ES$,$ EF$,$ LS$,$ LF$,$ and Slack for each activity. c$.$ Which activities form the critical path? d$.$ What is the estimated time of the critical path? e$.$ Calculate the expected time for each activity. Enter these values in the appropriate column in the table above. f$.$ Given the variance for each activity, what are the project variance and the standard deviation? g$.$ What is the probability of completion of the project before week $40?$