[機統] complementary events
題目可以直接看這裡 http://ppt.cc/7KmU
Suppose that X1, X2, . . . are random variables taking the values 0 and
1, and satisfying
P(Xn=1| X1 = i1, . . . , Xn-1 = in-1)>= ε
for all n >= 1 and all choices of i1, . . . , in-1 ∈ {0,1}.
Show that ε>0 then
1) P(Xn = 1 for some n) = 1
2) P(Xn = 1 for infinitely many n) = 1
提示看complementary event
第二個感覺 complement是{ Xn=0 for infinitely many n}
從conditional prob 好像可以推出 P(Xn=0)<1 for all n
所以P(Xn = 1 for infinitely many n) = 1
第一個的complement 我不太確定
for some n是指 for finitely many n嗎?
但是我還是不知道他的complement是什麼
想請教一下板友
謝謝
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※ 編輯: nourri 來自: 76.171.77.30 (04/08 07:00)
※ 編輯: nourri 來自: 76.171.77.30 (04/08 07:05)
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