課程名稱︰多變量統計分析
課程性質︰應數所數統組必修
課程教師︰陳宏
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2016/4/26
考試時限（分鐘）：15:30~17:20
試題 :
1. (25%)In class, we talk about the norm of the random projection approximately
maintained. By knowing that
2 2 2 2 3
P((1-ε)||x|| ≦||ψ(x)|| ≦(1+ε)||x|| )≧1-2exp(-(ε-ε)m/4),
p
where ε∈(0,1/2). For any u,v∈R with ||u||≦1 and ||v||≦1, give a
T T
probability upper bound on the following event holds {|u v-ψ(u) ψ(v)|>ε}.
2. (40%) If X and Y are chosen at random from -1 and 1 with probabilities 1/2,
i i
T T
respectively. Let X=(X ,...,X ) and Y=(Y ,...,Y ) . Denote the angle between
1 p 1 p
Y and X by θ.
1/2 1
(a) Show that P[|cos(θ)|>(log c) /√p]<