课程名称︰统计学导论
课程性质：数学系选修
课程教师︰郑明燕
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2017/4/27
考试时限（分钟）：110
试题 :
β
1. Let X be a random variable with cdf F(x) = 1 - exp(-αx ) for x ≧ 0
and F(x) = 0 for x < 0, where α > 0 and β > 0.
(a) (3 pts.) Show that F is a cdf.
(b) (3 pts.) Find the density of X.
(c) (4 pts.) Find the probabilities P(1 ≦ X < 2) and P(X = 3).
2. Let X and Y have the joint density
6 2
f(x,y) =