The total costs of a proposed project consist of fabrication costs and installation costs. Each cost is uncertain. Fabrication costs Probability Installation costs Probability $MM % $MM % 10 40% 5 25% 20 50% 10 60% 50 10% 30 15% 3.1. Assume that there is no correlation between fabrication and installation costs.

Calculate and tabulate the probability distribution of the total costs of the project.

1. What are

• the most likely total costs,
• the approximate 90th, 50th and 10th percentiles (the "P90", the "P50" and the "P10") from the "more than" cumulative distribution,
• the mean total costs and
• the standard deviation of the total costs? 

2. Assuming that you had to pick only one estimate of the total costs, which single measure would you use? Why?

3. Recalculate and tabulate the probability distribution of the total costs assuming perfect positive correlation between the fabrication costs and installation costs.Calculate the standard deviation of the total costs.

In answering question 3, assume that perfect positive correlation means that when the fabrication costs are low, medium and high, the installation costs are correspondingly low, medium and high.

In addition, assume

(a) that low fabrication costs and installation costs have a 40% probability,

(b) that medium fabrication costs and installation costs have a 50% probability and

(c) that high fabrication costs and installation costs have a 10% probability.

4. Recalculate and tabulate the probability distribution of the total costs assuming perfect negative correlation between the fabrication costs and installation costs. Calculate the standard deviation of the total costs.

In answering question 4, assume that perfect negative correlation means that when the fabrication costs are low, medium and high, the installation costs are correspondingly high, medium and low.

In addition, assume

(a) that the low fabrication costs and high installation costs case have a 40% probability,

(b) that the medium fabrication costs and medium installation costs case have a 50% probability and

(c) that high fabrication costs and low installation costs case have a 10% probability.

5. Comment on the standard deviations calculated in questions 1, 3 and 4. Why are they different?

6. Assume that you have continuous probability distributions of cost estimates of the components of a project. Each of the distributions is log-normal.

• What is the difference between the sum of the "P90"s from each of the "more than" distributions and the "P90" of the statistical sum of the distributions?
• What is the difference between the sum of the "P50"s from each of the "more than" distributions and the "P50" of the statistical sum of the distributions?
• What is the difference between the sum of the "P10"s from each of the "more than" distributions and the "P10" of the statistical sum of the distributions? Give reasons for the differences.