Thread: Problem 1.9
View Single Post
  #1  
Old 09-29-2015, 01:14 AM
kongweihan kongweihan is offline
Junior Member
 
Join Date: Sep 2015
Posts: 1
Default Problem 1.9

I'm working through this problem and stuck on (b).

Since P[u_n \geq \alpha] \leq e^{-s\alpha}U(s), we get
\prod_{n=1}^N P[u_n \geq \alpha] \leq (e^{-s\alpha}U(s))^N

We also know\prod_{n=1}^N P[u_n \geq \alpha] \leq P[\sum_{n=1}^N u_n \geq N\alpha] = P[u \geq \alpha]

Both terms in the desired inequality is bigger than the common term, so I don't know how these two inequalities can lead to the desired conclusion, what did I miss?

Also, in (c), why do we want to minimize with respect to s and use that in (d)?
Reply With Quote