政治大學中山所共同選修 課程名稱： 社會科學計量方法與統計－計量方法 Methodology of Social Sciences 授課內容：

1. 政治大學中山所共同選修 課程名稱： 社會科學計量方法與統計－計量方法 Methodology of Social Sciences 授課內容： Introduction to Econometrics and Some Basic Probability 日期：2003年10月2日

2. Ch.2 Some Basic Probability Concepts 1.Random variable: a variable whose value is unknown until it is observed. The value of a random variable results from an experiment；it is not perfectly predictable . • Discrete random variable: only a finite number of values, that can be counted by using the positive integers. • Continuous random variable: take any real value in an interval on the real number line. 政治大學 中山所共同選修 黃智聰

3. 2.Probability • What the values of a discrete random variable are listed with their chances of occuring, the resulting table of outcome is called a probability function or a probability density function. • Discrete: f(x)=p(X=x) , 0≦f(x)≦1 , Σf(xi)=1 政治大學 中山所共同選修 黃智聰

4. Continuous: f(y) can be represented by an equation the area under the probability density function corresponds to probability. F(y) F(y) P[a≦Y≦b] : y 政治大學 中山所共同選修 黃智聰

5. 1/(a-b) if a≦u≦b • F(u)= 0 otherwise 1 1= F(u) b-a 0 1 u 0.1 0.3 政治大學 中山所共同選修 黃智聰

6. 3.Joint Probability Density Function G 男=0 女=1 Political totals KMT=0 200 270 470 DPP=1 300 100 400 P Other=2 60 70 130 Gender total 560 440 1000 政治大學 中山所共同選修 黃智聰

7. G 邊際機率 Marginal Probability 0 1 • Joint probability function 0.2 0.27 0.47 0.40 0.13 0 1 2 P 0.3 0.10 0.06 0.07 0.56 0.44 1 F(P , G)=f(0 , 0)=0.2 f(0 , 1)=0.27 政治大學 中山所共同選修 黃智聰

8. 4.Independent random variables. • If X and Y are independent random variables, then f(x , y)=f(x)f(y) • 5.Covariance: The covariance literally indicates the amount of covariation exhibited by the tow random variable. • Covariance is difficult to interpret because it depends on the unit of measurement of the random variable. 政治大學 中山所共同選修 黃智聰

9. The meaning of covariation is revealed more clearing if we divide b/w X and Y by their respective standard deviations which is called correlation coefficient ρ. 政治大學 中山所共同選修 黃智聰

10. 6.Normal Distribution • It is very hard to calculate the probability defined as the area under p.d.f. -∞＜x＜∞ 政治大學 中山所共同選修 黃智聰

11. Therefore, transfer the random variable in order to make the new variable with 0 mean and 1 variance. 政治大學 中山所共同選修 黃智聰

12. 例 0 1 0.33 政治大學 中山所共同選修 黃智聰