Reference no: EM131051764

Question 1

Briefly explain the concepts of independence and dependence between two events.

Question 2

Consider the costs of two  project  items given in Fig. 2.1, with  identical discrete probability distributions. Theyare to be linearly added.

Fig. 2.1

	Item I
Cost ($M)		Probability
	13.0	0.150
	16.5	0.600
	20.0	0.250

	Item 2
Cost ($M)		Probability
13.0		0.150
16.5		0.600
20.0		0.250

(i) Assume independence between the two items.

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) of the
consequence of this total cost.

3. Plot the frequency distribution and cumulative probability distribution of the result.

(ii) Assume complete (100%) positive dependence between the costs.

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) of the consequence of this total cost.

3. Plot the frequency distribution and cumulative probability distribution of the result.

Question 3

(i) Assuming a modified probability distribution as given in Fig. 3.1, in which the cost of the second item is conditionally dependent on the first:

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) of the consequence of this total cost.

3. Plot the frequency distribution and cumulative probability distribution of the result.

Fig. 3.1

Risk 1
Cost ($M)	Probability
13.0	0.150
16.5	0.600
20.0	0.250

Risk 2
Cost ($M)	Probability
13.0	0.350
16.5	0.650
13.0	0.200
16.5	0.550
20.0	0.250
13.0	0.050
16.5	0.800
20.0	0.150

(ii) Comment on the calculations you have made in questions 2 and 3, explaining any key points of similarity or difference between the results (up to 300 words).

(iii) Discuss examples of when, in an engineering or technological project or process,you would expect to find examples of each of these three scenarios (independence between the costs of two items, complete positive dependence between the costs of two items, and conditional dependence of the cost of one item on another) (up to 300 words).

Further Information

Background reading material for this task may be found in Chapman and Ward, Chapter 11. For this question, you can consider the variables as having discrete probabilities (i.e., not continuous).