[試題] 97上 江金倉 統計導論 期中考
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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