課程名稱：統計學 課程性質：必修 課程範圍：ch1.2.5(不含Bayes' Theorem).6 +ch3:p.57.58.62.73.76.79.80.82+ch7:p.219~234 開課教師：黃子銘副教授 開課學院：商學院 開課系級：商院整開 考試日期(年月日)：2010.11.16. 考試時限(Mins)：似乎是三小時 不過大家都兩小時以內就交卷 試題本文：(考題有兩種版本 以下附其中一份) 1.(5pts) What is the level of measurement (nominal, ordinal, interval or ratio) for each of the following variables? (a) The number of cups of coffee sold at Starbucks each Sunday during 2008. (b) The courses offered by the department of statistics at NCCU (National Chengchi University) during2006, such as statistics, calculus, probability, etc. (c) The monthly average temperatures at Taipei over the past 21 years. (d) The ranking of NCCU in 2009 according to the QS World University Rankings. 2.(5pts) Suppose that we have a sample of scores with sample mean 60 and sample standard deviation1. At least what percentage of the scores are between 56 and 64? 3.(5pts) Suppose that we have a sample of scores with sample mean 60 and sample standard deviation1. Find a range that covers at least 70% of the scores using Chebyshev's theorem. 4.(5pts) For a sample of size 1000 with minimum 0, maximum 1 and sample standard deviation 0.1, determine the number of classes for drawing a histogram using Scott's rule. 5.(5pts) Suppose that X is a random variable with CDF F, where 0 if x<1; F(x) = { x/2 if 1<=x<=2; 1 if x>2. Find P(X = 1) and P(X = 1.5). Note: you may use the graph of F to solve this problem. The graph of F is given below.(省略圖) 6.(5pts) During the past 34 years, Virgin Atlantic Airways experienced no air accident in 23 years. Estimate the probability that Virgin Atlantic Airways experiences no air accident in ove year. Which concept of probability (classical or empirical probability) is used to make the estimate? 7.(5pts) A large company needs to hire a new president. There are 5 candidates who are equally qualified. 3 of the candidates are female. Suppose that the company decides to choose the president by lottery. (a) What is the probability that one of the female candidate is selected? (b) Which concept of probability did you use to obtain your answer for Part (a)? 8.(5pts) Suppose that X is a discrete random variable with PMF px, where 0.2 if x=0; px(x) = { 0.5 if x=1; 0.3 if x=4; 0 otherwise. Find P(1.5 < X < 4.5). 9.(5pts) Suppose that X is a continuous random variable X has PDF f, where 0 if x<1; f(x) = { 1/2 if 1<=x<=3; 0 if x>3. The graph of f is given below.(省略圖) Find P(1.5 < X < 2.5) and P(X = 2.5). 10.(5pts) Suppose that we have a box of 1000 items, and 4 of them are defective. Suppose that we randomly select two items one at a time with replacement. For i = 1 or 2, let Xi = { 1 if the i-th selected item is defective; 0 if the i-th selected item is not defective. Find the PMF for X1 and the PMF for X2. 11.(5pts) A student is taking history and calculus. The probabilities that the student will pass the two courses are 0.3 for history and 0.6 for calculus, and the probability for passing both courses is 0.18. What is the probability of passing at least one course? 12.(5pts) Suppose that we have a box of 1000 items, and 4 of them are defective. Suppose that we randomly select two items one at a time without replacement. Let A be the event that the first item is defective and B be the event that the second item is defective. Find P(B) and P(B1A). Are A and B independent? 13.(5pts) Suppose that X is a discrete random variable with PMF px, where 0.1 if x=0; px(x) = { 0.4 if x=1; 0.5 if x=2; 0 otherwise. Find the mean and variance of X. 14.(5pts) Suppose that S is a population of 1000 scores. A summary for the scores is given in the following table. score frequency 0 100 1 400 2 500 Find the population mean and population variance for S. 15.(5pts) Suppose that Ms Yu goes fishing every weekend, and she catches 4 fishes in 2 hours on average. Suppose that she plans to spend 2 hours on fishing this weekend. Let X be the nmber of fishes that she will catch this weekend. Propose a distribution for X and find the probability that X >= 1 using the proposed distribution. 16.(5pts) A manufacturer of keys knows that 5% of the keys that they made are defective. Suppose that we take a sample of 10 keys made by the manufacturer. Find the probability that at least one key is defective. 17.(5pts) Suppose that X ~ U(0,1). (a) What are E(X) and Var(X)? (b) Find a lower bound for P(0.06 < X < 0.94) using Chebyshev's theorem. (c) Find P(0.06 < X < 0.94). 18.(5pts) Suppose that X ~ N(0,1). Find the following probabilities using the N(0,1) table. (a) P(-0.51 < X < 1.5). (b) P(0.51 < X < 1.5). (c) P(X > 1.5). (d) P(X > -0.51). (e) P(X < 0.51). 19.(5pts) Suppose that S is a population and the population distribution for S is N(11,4). (a) What is the proportion of the values in S that are less than 14? (b) What are the population mean and variance of S? (c) Give a range such that 95% of the values in S are in the range using the empirical rule. 20.(5pts) Suppose that S is a population and the population distribution for S is Bin(1000,0.4). (a) What are the population mean and variance of S? (b) Give a range such that at least 75% of the values in S are in the range using Chebyshev's theorem. --

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