Differentiate between

i$.$ Critical Path Method $($CPM$)$ and the Project Evaluation and Review Technique in project network analysis

ii$.$ Risk Register and Risk Breakdown Structure

Briefly explain the role of the following: in project network analysis:

i$.$ Pessimistic time

ii$.$ Optimistic time

iii. Most likely time

State and discuss the rules applied to a "Forward Pass" in Network Analysis

Use the Table $1$ on the next page to answer the following questions:

i$.$ Using Network analysis determine the Critical Path of the Project

ii$.$ Calculate the planned duration on the project in months

iii. Identify any non$-$critical tasks and the floats$/$slack time on each task

TABLE $1$: Network Activities

$\backslash$table$[[$ACTIVITY$,$PREDECESSOR,$\backslash$table$[[$OPTIMISTIC$],[$TIME$],[($Months$)]],\backslash$table$[[$MOST$],[$LIKELY$],[$TIME$],[($Months$)]],\backslash$table$[[$PESSIMISTIC$],[$TIME$],[($Months$)]]],[A,-,5,7,9],[B,A,14,15,16],[C,B,23,25,27],[D,B,13,15,17],[E,B,28,30,32],[F,C,D,8,10,11],[G,E,F,10,12,14],[H,G,3,5,7],[I,H,2,4,6],[,,,,]]$

Using Table $1,$ draw the network diagram and determine the critical path in months

Given the Pessimistic and Optimistic Times, compute the expected times for each activity and

a$)$ the probability of completing the project in $72$ months; b$)$ for a probability of $95\%$ how many months will it take to complete the project?

i$.$ Compute the expected time $(t_e)$ and the variance $S^2$ for each activity

ii$.$ What is the standard Deviation of the Critical Path

iii. What is the probability that the project will be completed in

A$)72$ months

B$)78$ months

Explain the implication of each probability of completing the project within the giv$0.$en time.