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(math144)[2010](f)midterm~id-^_10461.pdf
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HKUST
MATH 144 Applied Statistics
Midterm Examination Name:
29th March 2010 Student I.D.:
19:00C21:00 Tutorial Section:

Directions:
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Write your name, ID number, and tutorial section in the space provided above.

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DO NOT open the exam booklet until instructed to do so.

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Turn o. all mobile phones and pagers during the examination.

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This is a closed book examination.

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Unless otherwise speci.ed, numerical answers should be either exact or correct to 4 decimal places.

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You are advised to try the problems you feel more comfortable with .rst.

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You may write on both sides of the examination papers.

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You must show the working steps of your answers in order to receive full points.

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You must not possess any written or printed papers that contains information related to this examination.

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Cheating is a serious o.ense. Students caught cheating are subject to a zero score as well as additional penalties.


Question No. Points Out of
Q. 1 20
Q. 2 20
Q. 3 10
Q. 4 10
Q. 5 10
Q. 6 20
Q. 7 10
Total Points 100

Answer ALL questions on the space provided.
1. [ 20 Marks ] The nicotine contents, in milligrams, for 35 cigarettes of a certain brand were recorded as follows:
1.19 1.71 1.58 2.11 1.64 1.92 1.47 2.03 1.86 1.72 2.31 1.97 1.70 1.90 1.69 1.79 1.05 -2.17 1.63 1.85 2.28 1.24 1.75 1.51 1.82 1.79 1.75 1.37 1.40 1.69 2.37 2.08 1.93 1.64 2.09

(a)
[3] Construct a stem plot with the leaf unit of 0.01. (For instance, we use 17|9 to represent 1.79)

(b)
[10] Construct a boxplot with full description. Are there any potential outliers shown in the boxplot? If yes, then what are they? and please comment whether you have enough evidence to conclude that the potential outlier(s) is an outlier(s) or not?

(c)
[7] Remove the outlier found in (b), and then reconstruct a boxplot with full description.


2. [20Marks]
(a)
[8] If 3 married couples are seated randomly at a round table, then .nd the probability that no couple can sit together.

(b)
(*) Consider n married couples. What is the probability that there are r couples sitting together, where r n, if the n couples are seated randomly


i. [6] at a round table;
ii. [6] in a row.
3. [ 10 Marks ] A structure has been designed to withstand up to a maximum wind speed x0 km per hour, which can be exceeded once every N = 10 years. In other words, the return period is N = 10 years for the the design parameter x0. Suppose that the annual maximum wind speed X can be represented by an exponential random variable with mean 75 km per hour.
(a)
[3] Find the value of x0. (Hint: x0 satis.es P (X>x0)=1/N).

(b)
[5] What is the probability that the structure will be exposed at least twice to a maximum annual wind speed larger than 0.9x0 in the .rst 8 years.

(c)
[2] What would be return period for the structure if the design parameter x0 is