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：數學系
考試日期（年月日）：2010/11/05
考試時限（分鐘）：120 mins
是否需發放獎勵金：是
（如未明確表示，則不予發放)
Introduction to Statistics(Midterm)
1. (24%) State or define the following terms:
(1a) Howthone effect. (1b) Bayes rule. (1c)probability function.
(1d) random variable. (1e) mutually independent events. (1f) odds ratio.
2. (10%) Let rXY be the pearson correlation coefficient of the sample
{(X1,Y1), … , (Xn,Yn))}.Show that |rXY|1.
3 Let X be the scores of an entrance examination, which has a continuous
distribution with men 6- and standard deviation 5.
(3a) (5%) What is the probability of 60 score?
(3b) (5%) What is the original score of Z=2?
(3c) (5%) Suppose that the cumulative distribution of Z, Say, Φ(z)=P(Z≦z)
is known.Express the probability of the score between 50 and 70 via
the cumulative distribution function Φ(z).
4,(3%)(4%) Are two independent events mutually exclusive? Explain your answer.
5.(8%) Let fx(x) be the probability density function of a continuous random
variable X .Write the rth central moment of X.
6.(6%) Write the properties of a cumulative distribution function.
7.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!}[0,1,….](x), where λ≦0.
(7a)(8%) State the assumptions of a Poisson distribution.
(7b)(7%) Let Y be the number of students entering the library within one hour.
Write the probability distribution of Y.
8.(7%)(7%) 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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