President of Gentech Construction, has developed the tasks, duration, and predecessor relationship for his new project in the following table $($times in weeks$)$:

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessor$]],\backslash$table$[[$Optimistic$],[($weeks$)]],\backslash$table$[[$Most Likely$],[($weeks$)]],\backslash$table$[[$Pessimistic$],[($weeks$)]]],[$A$,-,4,8,12],[$B$,$A$,10,15,26],[$C$,$A$,8,12,16],[$D$,$A$,4,6,14],[$E$,$B$,1,2,3],[$F$,$E$,$C$,4,7,10],[$G$,$E$,$C$,2,3,4],[$H$,$F$,2,2,2],[$I$,$F$,6,6,6],[$J$,$D$,$G$,$H$,3,6,15],[$K$,$I,J$,6,7,8]]$

Calculate the expected activity time and the variance for all activities.

Draw a project network $($AON$)$ and find ES$,$ EF$,$ LS and LF time for each activity.

What is the completion time and the critical path of the project?

What is the probability that the project will be completed before a $52$ weeks dead$-$line?

What is the probability that the project will be completed before a $42$ weeks dead$-$line?

What should be the dead$-$line of the project if the probability to finish within that time frame would be $90\%?$

P$3-2$