b$)$ The network diagram for a project is shown in the accompanying figures in table $2$ below, with three time estimates for each activity. Activity time are in a weeks. Do the following:

Table $2$

$\backslash$table$[[$Activity$,\backslash$table$[[$Optimistic time$],[($a$)]],\backslash$table$[[$Most likely$],[($m$)]],\backslash$table$[[$Pessimistic$],[$time $($b$)]],\backslash$table$[[$Immediate$],[$Predecessor$($s$)]]],[$A$,3,6,8,-],[$B$,2,4,4,-],[$C$,1,2,3,-],[$D$,6,7,8,$C$],[$E$,2,4,6,$B$,$D$],[$F$,6,10,24,$A$,$E$],[$G$,1,2,4,$A$,$E$],[$H$,3,6,9,$F$],[$I$,10,11,12,$G$],[$J$,14,16,20,$C$],[$K$,2,8,10,$H$,$I$]]$

i$.$ Compute the expected time for each activity and the expected duration for each path.

ii$.$ Identify the critical path

iii. Compute the variance of each activity and the standard deviation of each path.

$(20$ Marks$)$