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EMSE 6020: Decision Making with Uncertainty
HOMEWORK 4, SUMMER 2013
Instructor: Joost Santos
DEADLINE: June 27, 2013
Problem 1: (2 pts)
Two contractors (1 and 2) placed a bid on a road construction project. They were each asked to provide percentile estimates of the time (x, in years) it would take the road to undergo a major maintenance after its completion. We seek to maximize this time variable x, as larger values imply better structural integrity as well as cheaper projection of the net present value for maintenance cost.
The CDF for contractor 1, F1(x) is as follows: x 20
25
40
45
50
F1(x)
0.00
0.25
0.50
0.75
1.00
The CDF for contractor 2, F2(x) is as follows: x 10
30
40
45
50
F2(x)
0.00
0.25
0.50
0.75
1.00
(a) Graph the CDF for each contractor.
(b) Calculate analytically the expected value of x for each contractor. [Hint: See Slide #27 on
Module 9]
(c) Based alone on your computed expected values from (b), which contractor would you recommend? (d) What analysis can you supplement with (c) to improve your recommendation?
Page 1 of 2
Problem 2: (1 pt)
The number of cyber attacks
HOMEWORK 4, SUMMER 2013
Instructor: Joost Santos
DEADLINE: June 27, 2013
Problem 1: (2 pts)
Two contractors (1 and 2) placed a bid on a road construction project. They were each asked to provide percentile estimates of the time (x, in years) it would take the road to undergo a major maintenance after its completion. We seek to maximize this time variable x, as larger values imply better structural integrity as well as cheaper projection of the net present value for maintenance cost.
The CDF for contractor 1, F1(x) is as follows: x 20
25
40
45
50
F1(x)
0.00
0.25
0.50
0.75
1.00
The CDF for contractor 2, F2(x) is as follows: x 10
30
40
45
50
F2(x)
0.00
0.25
0.50
0.75
1.00
(a) Graph the CDF for each contractor.
(b) Calculate analytically the expected value of x for each contractor. [Hint: See Slide #27 on
Module 9]
(c) Based alone on your computed expected values from (b), which contractor would you recommend? (d) What analysis can you supplement with (c) to improve your recommendation?
Page 1 of 2
Problem 2: (1 pt)
The number of cyber attacks