作者buttermilk (脱脂牛奶)
看板Statistics
标题[问题] 一题机率论的定理证明
时间Wed May 2 15:44:04 2007
Let {X_n} be a sequence of random variables bounded in probability and
let {Y_n} be a sequence of random variables which converge to 0
P
in probability. Then X_nY_n ------> 0.
Proof:
Letε> 0 be given. Choose B_ε> 0 and an integer N_ε such that
n≧N_ε => P[∣X_n∣≦B_ε]≧1-ε.
Then,
--- ---
lim P[｜X_nY_n｜≧ε]≦ lim P[｜X_nY_n｜≧ε,∣X_n∣≦B_ε]
n→∞ n→∞
---
+ lim P[｜X_nY_n｜≧ε,∣X_n∣＞B_ε]
n→∞
---
＜ lim P[｜Y_n｜≧ε/B_ε] + ε = ε
n→∞
From which the desired result follows.
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从 Then 後面的式子就看不懂了。
另外，
---
为什麽它是取 lim 而不是取 lim ，机率收敛的定义不是要用 lim 吗？
n→∞ n→∞ n→∞
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