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 critical 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.

1) Randomly sample 100 observations for both discrete triangular distributions of each task. Create a RV that is the sum of the tasks for each 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 0. (Hint: there should be 9 bin values, 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)?