Question $1)(30$ points$)$

$\backslash$table$[[$Symbol$,$Immediate Predecessors,Time estimat$],[,-,15],[$A$,-,25],[$B$,-,],[$C$,$A$,3],[$D$,$C$,7],[$E$,,1],[$F$,$B$,5],[$G$,$D$,$F$,2],[$H$,$D$,$F$,4],[$I$,$E$,$F$,10],[$J$,,8],[$K$,$G$.$J$,]]$

a$.(7\mathrm{.}5$ points$)$ Draw the AOA network for this project

b$.(7\mathrm{.}5$ points$)$ Calculate the total slacks and interpret the meaning; calculate critical path and interpret the meaning.

c$.(15$ points$)$ Suppose that activities D$,$ E$,$ F are subject to uncertainty and that only the following time estimates are available. Calculate the probability that the project will be completed in days, for $d=52,53,56$ plot the probability as a function of $d$

$\backslash$table$[[$Activity$,$a$,$m$,$b$],[$D$,2,4,5],[$E$,5,6,9],[$F$,1,3,4]]$