課程名稱︰統計導論 課程性質︰選修 課程教師︰江金倉 開課學院：理學院 開課系所︰神經生物與認知科學學程 數學系 考試日期（年月日）︰2008年11月10號 考試時限（分鐘）：120分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(15%) Distinguish between each of the following paired terms. (1a) retrospective study versus prospective study. (1b) confounding variable versus interacting variable. (1c) categorical variable versus discrete variable. (1d) statistic versus parameter. (1e) case-control versus matched-paired design. 2.(5%)(5%) Compute the mean and variance of the grouped data with f1,f2,…,fg being the frequencies of the g classes [a0,a1),[a1,a2),…,[ag-1,ag]. 3.Let rXY be the correlation coefficient of the sample {(X1,Y1),…,(Xn,Yn)} (3a)(2%)(2%)(3%) Explain the meanings of rXY=1,rXY=-1, and rXY=0,respectively (3b)(8%) Consider the re-scaled data {(U1,V1),…,(Un,Vn)} with Ui=aXi+b and Vi=cYi+d, where a and c are positive constants and b and d are any constants. Show that the correlation coefficient rUV is same with rXY 4.(6%)(4%) Write the definitions of probability function and random variable. 5. Let A and B be mutually independent events. (5a)(2%)(3%) Are A and B mutually exclusive? Explain your answer. (5b)(5%) Suppose that the probabilities of A and B are known. What is the probability of A∪B? 6.(4%)(6%) In the AIDS study, let D and T denote separately the events of HIV+ patients and patients who are diagnosed as HIV+ patients. Suppose that the positive predictivity P(D|T) and the negative predictivity P(D^c|T^c) are known. What additional condition is required to compute the sensitivity P(T|D) and the specificity P(T^c|D^c)?How to compute the sensitivity and specificity? 7.(5%) Let fX(x) be the probability density function of a continuous random variable X. Write the rth central moment of X. 8.(5%) Consider the probability mass function f(x) of random variable X with the corresponding probabilities 0.1, 0.3, 0.1, 0.2, and 0.3 at x=1, 2, 3, 4, and 5. Compute the probability of {1＜X≦3.5} 9. Let X be the number of students entering the library of the NTU every thirty minutes. Suppose that X follows a Poisson distribution fX(x)=(λ^x)*(e^(-λ))/x! 1 (x), where λ＞0. {0,1,…} (9a)(8%) State the assumptions of a Poisson distribution. (9b)(7%) Let Y be the number of students entering the library within one hour. Write the probability distribution of Y. 10.(7%)(8%) An experiment consists of a sequence of independent coin tosses. Let X denote the number of heads occurring within n tosses and Y be the number of tails occurring before the rth head. Write the probability density functions of X and Y --

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