Consider the network described in the table below. Summarize your answers in the table below. Show all your work otherwise no credit given. Ten points $($network $2$ points, part a$+$b$-6$ points, part c$-2$ points$).$ If using software as evidence of your work please provide relevant software output data. Activity A$,$B$,$C$,$D$,$E$,$F$,$G$.$ Immediate Predecessor$($s$)--,--,$A$,$A$,$BD$,$BD$,$CE$.$ Pessimistic $15,9,11,10,9,11,12.$Probable $10,8,6,8,5,7,8.$Optimistic $8,7,5,4,1,4,3.$ a$)$Calculate the expected duration of each activity. b$)$ Calculate the expected duration and variance of the critical path. c$)$ Calculate the probability that the project will be completed in fewer than $30$ time units