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EMSE 6020: Decision Making with Uncertainty

HOMEWORK 4, SUMMER SEASON 2013

Trainer: Joost Santos

DEADLINE: 06 27, 2013

Problem one particular: (2 pts)

Two contractors (1 and 2) positioned a bid on a road structure project. These were each asked to provide percentile estimates of the time (x, in years) it will take the road to undergo a serious maintenance after its achievement. We seek to maximize on this occasion variable by, as larger values suggest better structural integrity and also cheaper discharge of the net present worth for routine service cost.

The CDF intended for contractor you, F1(x) can be as follows:

back button

20

twenty-five

40

forty five

50

F1(x)

0. 00

0. twenty-five

0. 55

0. seventy five

1 . 00

The CDF for service provider 2, F2(x) is as follows:

x

10

30

45

45

60

F2(x)

zero. 00

0. 25

zero. 50

zero. 75

1 ) 00

(a) Graph the CDF for every contractor.

(b) Calculate analytically the expected value of x for each and every contractor. [Hint: Observe Slide #27 on Module 9]

(c) Primarily based alone on your own computed anticipated values by (b), which will contractor will you recommend?

(d) What analysis can you health supplement with (c) to improve the recommendation?

Webpage 1 of 2

Problem two: (1 pt)

The number of cyber attacks (𝑋) to E-Lake, an online market site, is usually Poisson with mean appearance rate of 30 attacks per hour. Demonstrate detailed computations to answer the subsequent: (a) Precisely what is the probability that there is no attack over the following minute? (b) Calculate the minimum worth of 𝑥 (per minute) that fulfills Pr 𝑋 ≤ 𝑥 > 0. 98. (c) Suppose the time between every attack can be exponentially sent out with the same mean arrival rate given previously. Starting at t=0 (when the auction site opens their business in a given day), what is the probability of an attack inside the first half a minute? (d) Determine the median time, in seconds.

Problem 3: (2 pts)

A network officer is looking at two contradictory alternatives for an attack detection program, A and B. The reliability allocation of the devices are triangulado, with guidelines:

A:...

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