Question 2 (50 marks total) Question 2(a) Consider the cost probability distributions for following two project items (Item 1 and Item 2) in Table 2.1. The costs of the two project items are to be linearly added. Table 2.1 Project Item 1 Cost (SM) Probability Project Item 2 Cost (SM) Probability 30.00 40.00 45.00 0.250 0.520 0.230 55.00 65.00 70.00 0.320 0.460 0.220 Assume independence between the costs of the two cost items. 1. Calculate the points of the combined probability distribution of total cost of the two items. 2. Calculate mean (expected value) and variance of the consequence of this total cost. 3. Plot the frequency distribution and cumulative probability distribution of the result. (15 marks) Question 2(b) Assume a modified probability distribution as shown in Table 2.2, in which the cost of the second project item is conditionally dependent on the cost of the first project item: 1. Calculate the points of the combined probability distribution of total cost of the two items. 2. Calculate mean (expected value), variance and mode (most likely value). 3. Plot the frequency distribution and cumulative probability distribution of the result. (20 marks) Table 2.2 Project Item 1 Cost (SM) Probability Project Item 2 Cost (SM) Conditional Probability 35.00 0.250 55.00 65.00 70.00 0.260 0.460 0.280 40.00 0.520 55.00 65.00 70.00 0.190 0.520 0.290 45.00 0.230 55.00 65.00 70.00 0.150 0.550 0.300 Question 2C) Using an example engineering project or process of your choice, and the results of your calculations for this question to support your answer, discuss, in about 400 words, why it is important, when analysing and assessing project or project risks, to have an understanding of the potential range of risks, and be able to combine risks of a number of project activities to develop a risk profile of your selected project or process? (15 marks)