課程名稱︰統計學導論
課程性質：數學系選修
課程教師︰鄭明燕
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2017/4/27
考試時限（分鐘）：110
試題 :
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) =