Problem $1$: $(45$ points$)$ The time unit is day. $($Show your work$)$

$\backslash$table$[[-$Act,Pred,a$,$m$,$b$,$Exp t$,$Var,ES$,$EF$,$LS$,$LF$,$Slack,If Crash,Crash $$,$C$.$ rate,Crash by$,$$$],[$A$,-,10,15,19,,,,,,,,0,0,,,],[$B$,-,19,25,28,,,,,,,,5,1000,,,],[$C$,$A$,18,18,18,,,,,,,,4,1600,,,],[$D$,$A$,$ B$,7,13,19,,,,,,,,3,1800,,,],[$E$,$B$,16,18,20,,,,,,,,3,900,,,],[$F$,$D$,15,19,22,,,,,,,,2,800,,,],[$G$,$E$,$ F$,14,20,26,,,,,,,,5,2500,,,]]$

Draw AON network with ES$,$ EF$,$ LS$,$ LF; Fill the table; Show Critical path;

What is the expected project completion time and what probability to complete it in exactly such time?

What is the project completion standard deviation and variance?

Crash the project to $5$ days down.

Give the duration of project with $99\%$ probability.

What is the probability of finishing the project in less than $80$ days?