請自選二類題作答，並請標示答類號。
	第一類：工程統計
1.	Suppose that customers arrive to a system independently. The number of arriving customers per hour follows a Poisson process with rate 20 customers per hour. (3 points each) (a) What is the expected number of customers that arrival during 90 minutes. (b) Suppose that exactly 10 customers arrive during the first hour, half of the expected rate. Let X denote the number of customers that arrive in the next hour. Then what is the distribution of X ? (c) What is the probability that the time between two consecutive customers is more than 5 minutes? (d) Let Y denote the time between the second and the tenth customer. What is the distribution of Y ?
2.	Let X be the time (in months) until failure of a specific type of equipment. Define p as the proportion of equipments that have times until failure larger than 4 months, i.e., p = P{X > 4}. Fifty equipments of the same type are tested and their times until failure are recorded. (a) Assume that X is exponentially distributed with mean 5 months. Define Y as the number of the 50 observations, times until failure, that are larger than 4. What is the value of p? What is the probability distribution of Y? (7 points) (b) Assume that the distribution of X is unknown. Suppose that 30 out of the 50 tested equipments have times until failure larger than 4. Is there sufficient evidence that the value of p is larger than 0.5? Test using α= 0.01. (9 points) (c) If p = 0.55, what is the probability of Type II error for Question 2(b)? (7 points)
3.	Let X1,…, X5 be a sample from uniform(θ-2 , θ+2 ) . Define and Xmed as the sample mean and sample median. (5 points each) (a) Find the mean, variance, and mean squared error of , denoted as MSE( ). (b) Find the mean, variance, and mean squared error of Xmed , denoted as MSE(Xmed). (c) Compute the relative risk MSE( )/MSE(Xmed).
	第二類：作業研究
1.	(25%) Identify the decision variables and formulate an Linear Programming model for the following problem. A vineyard wishes to blend wine of five different years (i = 1,2,…5) to make three types of blended wine. The available supply(in gallons) of wine from year i is Si, i = 1,2,…5. Blend 1 is considered a premium blend and, therefore, no more than 100 gallons are to be made. Restrictions on each of the blends are given in the following table. Blend Restriction Profit per gallon 1 At least 60% must be from years 1 and 2, no more than 10% from year 4 and 5 c1 2 At least 50% must be from year 1, 2, and 3 c2 3 No more than 50% from year 5 c3
2.	(25%) Consider the following Markov Chain problem. Suppose the manufacturer of a brand of coffee is considering an extensive advertising campaign design to cause consumers to try his brand of coffee. From panel data obtained through market research, he has been able to estimate the current probabilities of consumers changing from "our brand" to "any other' and vice versa, as given in Table 1. Also, suppose that market researchers have estimated the corresponding probabilities that will exist after the advertising campaign has taken place (see Table 2). Note that the probability of customers switching from "any other" to "our brand" has increased from 0.2 to 0.3, but the probability of retaining our current customers has not changed. Table 1. Probabilities of changing brands of coffee ( no advertising campaign)   Our brand (state 0) Any other (state 1) Our brand (state 0) 0.8 0.2 Any other (state 1) 0.2 0.8 Table 2. Probabilities of changing brands of coffee (after advertising campaign)   Our brand (state 0) Any other (state 1) Our brand (state 0) 0.8 0.2 Any other (state 1) 03 0.7 Suppose that the advertising campaign will cost $12 million per year, and that there are 50 million coffee purchasers in the market. For each customer the average annual profit before taxes is $2. Should the manufacturer undertake the advertising campaign?
	第三類：計算機概論
1.	(10%) Describe the differences between HTML and XML, and discuss their applications.
2.	(10%) Describe the differences between SET and SSL, and discuss their applications.
3.	(15%) Explain the following terminology: (A) TCP/IP (B) MIME (C) Data Mining (D) Firewall (E) Data Warehouse
4.	(15%) An integer array A[n] is given with any size of n. (A) Write a program (specify the programming language you choose) for determining the result of difference between the maximal even number and the minimal odd number in the array. (12%) (B) Test your program with the following data: A[] = [ 33, 2, 4, 12, 11, 5, 8, 45] (3%)
	第四類：案例分析
1.	對公司而言，常存在不同等級的決策，如策略面(strategic)、戰術面(tactical)和作業面(operational)。此三等級決策所橫跨的時間面(time horizon)不同，在決策下達的層次上也常有先後關係，然而，此三者應相互配合，否則上層的決策恐無法貫徹於下層，下層亦無法反映執行狀況於上層。請討論應如何配合？(15%)
2.	承接前題的概念，現場作業人員、生產部經理、總經理(或董事長)所專注的績效，各自有其使用的指標(Keep Performance Index, KPI)，如現場作業人員在乎機器稼動率，總經理(或董事長)則在乎市場佔有率，試以高科技產業或中型傳統產業為例(擇一即可)，列舉常用的KPI，並請討論這些屬於各階層的KPI是否能相互轉換？若不能適當地轉換時，會產生什麼問題？(20%)
3.	業務部和生產部常在接單與否及生產負荷上出現不同的意見，請建議可建立何種機制以簡化兩部門間的歧見？(15%)

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