| ■可使用計算機，惟僅限不具可程式及多重記憶者 □不可使用計算機 |
注意事項: 本考試科目可分成兩大部份(Part I ，Part II)，各佔50分:
(Part I)工業工程專業論文分析-請從四篇論文中，自選一篇作答
(Part II)請從工程統計、作業研究、計算機概論三類課題中，自選一類作答 |
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| (Part I) 工業工程專業論文分析 |
| 1. |
(10%) Specify the title of the paper and identify the purpose
of the paper |
| 2. |
(10%) Describe the proposed approach of the paper |
| 3. |
(10%) Identify the contributions of the paper |
| 4. |
(10%) Discuss the limitations or drawbacks of the paper |
| 5. |
(10%) Discuss the extensions of the paper |
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論文一 論文二 論文三 論文四 |
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| (Part II-1) 工程統計 |
| 1. |
(10%) Suppose that 
constitute a random sample from a uniform distribution on (0,  ).
What is the maximum likelihood estimator of ?
Note: The density function of the uniform distribution is  . |
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| 2. |
An electronic part consists of two components. If one of the
two components fails, the electronic part fails. Suppose that the lifetime
 for
the first component is distributed as exponential with mean 10 hours and
the lifetime 
for the second component, independent of the first component, is distributed
as exponential with mean 20 hours. Note: The density function of an exponential
distribution with mean is
 , . |
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(a) |
(15%) What is the probability that the lifetime of the electronic
part exceeds 15 hours? |
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(b) |
(15%) What is the probability that the first component fails
before the second component? |
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(c) |
(10%) Suppose that 5 such electronic parts are used simultaneously.
What is the probability that there are at least three electronic parts working
after 15 hours of using the parts? |
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| (Part II-2) 作業研究 |
| 1. |
(10%) Find necessary and sufficient conditions for s to make
the LP problem
have an exactly one optimal solution, multiple optimal solution or to make
this problem infeasible and unbounded. |
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| 2. |
(10%) Prove that if a LP problem has exactly one optimal solution
then it must be a corner-point feasible solution. |
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| 3. |
(10%) Consider a irreducible ergodic Markov chain with transition
probability  .
Let 
be the limiting probability. Show that  . |
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| 4. |
(20%) Two players, A and B, are to play a best of series of
games and the one who wins 4 games will win the competition. Suppose the
results of games are iid and each game is won by A with probability p. Let
the state of the system be (a,b), where a is the number of games won by
A and b is the games won by B. Specify the transition matrix and find the
probability that A will win the competition. |
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| (Part II-3) 計算機概論 |
| 1. |
(10%) Describe the difference between web application and
web service. |
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| 2. |
Many programs written with inheritance could be written with
composition instead, and vice versa. Create an example with pseudo-codes
to demonstrate this (for instance, Point, Circle and Cylinder
classes). (10%) After you do this, assess the relative merits of the two
approaches, as well as for object-oriented programs in general. (5%) Which
approach is more natural? (5%) Why? (5%) |
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| 3. |
(15%) You are visiting the zoo one day, when you realize that
the map they give you is, in fact, a graph! It even has 'weights' on it,
which stand for the approximate time (in minutes) that it takes to walk
around between the cages, as shown in the following figure. Perform a Breadth
First Search (BFS) from the (yawn) Lions to the exciting Plankton showcase.
Write down all the animals you see along the way. Then write the path that
your search finds through the zoo. For lack of a better system, you decide
to visit animals in alphabetical order, when possible. |
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