$5-5$ In the following table, task durations are given in weeks. The estimates were made at the $95$ percent level $($see Section$\mathrm{.}5\mathrm{.}2,$ Calculating Probabilistic Activity Times subsection$).$

$\backslash$table$[[$Activity$,$Predec.,Opt.,Norrmal,Pess.$],[$a$,-,2,4,6],[$b$,-,3,5,9],[$c$,$A$,4,5,7],[$d$,$A$,4,6,10],[$e$,$b$,$ c$,4,5,7],[$f$,$D$,3,4,8],[$g$,$e$,3,5,8]]$

a$.$ Find the expected time and variance for each task.

b$.$ Draw the network $($either AOA or AON$)$ and find the path with the longest expected time. What is the expected time to complete this path?s