
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
December 3rd, 2016, 02:57 AM  #1 
Senior Member Joined: Feb 2015 From: london Posts: 121 Thanks: 0  Expectations
$\displaystyle S_n$ where n>=0 represents a renewal $\displaystyle N(t)$ represents the number of renewals up to time t $\displaystyle E[N(t)] = \sum_{n=1}^{\infty} P(N(t) >= n )$ (1) $\displaystyle E[N(t)] = \sum_{n=1}^{\infty} P(S_n <= t )$ (2) $\displaystyle E[N(t)] = \sum_{n=0}^{\infty} P(S_{2n+1} <= t ) +\sum_{n=1}^{\infty} P(S_{2n} <= t )$ (3) Can anyone please explain to me how you go from (2) > (3)? 
December 3rd, 2016, 07:06 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807 
Sum (2) is over all subscripts. Sum (3) separates that into a sum over all odd subscripts and a sum over all even subscripts.

December 10th, 2016, 01:21 AM  #3 
Senior Member Joined: Feb 2015 From: london Posts: 121 Thanks: 0 
Thanks, that make sense.


Tags 
expectations 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Expectations  Dima84  Algebra  0  January 14th, 2014 08:56 AM 
Query on expectations.  kaushiks.nitt  Advanced Statistics  1  January 18th, 2013 06:13 PM 
Expectations of a Random Variable  MarcoEcon  Algebra  3  November 19th, 2012 04:53 AM 
Simple Distribution & Expectations >_<  Aeonitis  Advanced Statistics  3  August 5th, 2010 03:57 PM 