O Final Prob4.) The manager of a project determined some time ago that the most critical task in the timely completion of a project is the use of a special instrument, a confusitron, that has an uncertain completion time (a ramdom variable in terms of hours). He asks you, a confusitron expert, to use your experience to specify a discrete triangular probability distribution of outcomes --most like time to complete, pessimistic time to complete, and optimistic time to complete. Recently the project manager has learned that there is another equally critica I task-framis- validation. This task cccurs immediately after the confusitron. You are also a framis-validation expert. The project manager asks you for a similar discrete triangular distribution of outcomes (see below). He then asks you to create a random sample of 100 observations from this distribution: Confusitron Distribution of Hrs. Framis -Validation Distribution of Hrs. hrs. hrs. prob. 0.1 optimistic 30 prob. 0.15 0.55 40 most likely 0.65 optimistic most likely pessimistic 0.3 42 60 pessimistic 0.25 80 95 observation 100 observations for both discrete triangular distributions of each task. Create a RV that is the sum of the tasks for each 1) Randomly sample observation. Place the results in the designated area below. 2) Create a frequency distribution column graph of the 100 Sum observations below by determining the Sample Space for the RV; so, the bins for the column graph will be the unique sample space values of the graph. Make the first bin O. (Hint: there should be 9 bin valu es, including 0) 3) What is the expected value of the Sum distribution? There are 2 theoretical ways to calculate it. Does it approximately match the average of your 100 observations (as it should)? Dist. of Confusitron Time Dist. of Framis-Validation 0.7 0.6 05 0.5 04 04 03 03 02 0.2 0.1 01 42 95 Confusitron Framis O Table for VLOOKUP Sampling Table for VLOOKUP Sampling Interval for Ou Outcome 0.00 0.10 30 Interval for Ou Outcome 0.00 0.15 40 0.10 0.75 42 0.15 0.70 60 0.75 1.00 80 0.70 1.00 95 0 Randomly Selected Times obs Confusitro Framis Sum 40 prob. optimistic 0.1 most likely 0.65 pessimistic 0.25 06 05 04 03 02 01 0 40 hrs. 30 42 80 prob. hrs. optimistic 0.15 most likely 0.55 pessimistic 0.3 Dist, of Framis-Validation 40 60 95 60 95 Dist of Framis-Validation 03 O O Final Prob4.) The manager of a project determined some time ago that the most critical task in the timely completion of a project is the use of a special instrument, a confusitron, that has an uncertain completion time (a ramdom variable in terms of hours). He asks you, a confusitron expert, to use your experience to specify a discrete triangular probability distribution of outcomes --most like time to complete, pessimistic time to complete, and optimistic time to complete. Recently the project manager has learned that there is another equally critica I task-framis- validation. This task cccurs immediately after the confusitron. You are also a framis-validation expert. The project manager asks you for a similar discrete triangular distribution of outcomes (see below). He then asks you to create a random sample of 100 observations from this distribution: Confusitron Distribution of Hrs. Framis -Validation Distribution of Hrs. hrs. hrs. prob. 0.1 optimistic 30 prob. 0.15 0.55 40 most likely 0.65 optimistic most likely pessimistic 0.3 42 60 pessimistic 0.25 80 95 observation 100 observations for both discrete triangular distributions of each task. Create a RV that is the sum of the tasks for each 1) Randomly sample observation. Place the results in the designated area below. 2) Create a frequency distribution column graph of the 100 Sum observations below by determining the Sample Space for the RV; so, the bins for the column graph will be the unique sample space values of the graph. Make the first bin O. (Hint: there should be 9 bin valu es, including 0) 3) What is the expected value of the Sum distribution? There are 2 theoretical ways to calculate it. Does it approximately match the average of your 100 observations (as it should)? Dist. of Confusitron Time Dist. of Framis-Validation 0.7 0.6 05 0.5 04 04 03 03 02 0.2 0.1 01 42 95 Confusitron Framis O Table for VLOOKUP Sampling Table for VLOOKUP Sampling Interval for Ou Outcome 0.00 0.10 30 Interval for Ou Outcome 0.00 0.15 40 0.10 0.75 42 0.15 0.70 60 0.75 1.00 80 0.70 1.00 95 0 Randomly Selected Times obs Confusitro Framis Sum 40 prob. optimistic 0.1 most likely 0.65 pessimistic 0.25 06 05 04 03 02 01 0 40 hrs. 30 42 80 prob. hrs. optimistic 0.15 most likely 0.55 pessimistic 0.3 Dist, of Framis-Validation 40 60 95 60 95 Dist of Framis-Validation 03 O