
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 20th, 2018, 11:14 AM  #1 
Newbie Joined: Apr 2018 From: New Jersey Posts: 1 Thanks: 0  How to expand a double sum of products express?
Please excuse me if this is in the wrong sub forum. Specifically, I need to expand this *unexpected loss for a portfolio* expression in order to calculate: $$S=\sqrt{(\sum_{i=1}^2\sum_{j=1}^2 w_i w_j u_i u_j ρ_{ij})}$$ I've attempted to expand it on my own, coming up with: $$\sqrt{(w_i*w_i*u_i*u_i*ρ_{ij} + w_j*w_j*u_j*u_j*ρ_{ij})}$$ Am I expanding this expression correctly? Thanks! 
April 20th, 2018, 12:57 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,823 Thanks: 723 
No. You want $\sqrt{w_1w_1u_1u_1\rho_{11}+w_1w_2u_1u_2(\rho_{12 }+\rho_{21})+w_2w_2u_2u_2\rho_{22}}$

April 22nd, 2018, 12:52 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
$\displaystyle \sum_{i=1}^2\sum_{j=1}^2 w_iw_ju_iu_jp_{ij}= \sum_{i=1}^2\left(\sum_{j=1}^2 w_iw_ju_iu_jp_{ij}\right)= \left(\sum_{j=1}^2 w_1w_ju_1u_jp_{1j}\right)+ \left(\sum_{j=1}^2 w_2w_ju_2u_jp_{2j}\right)= \left(w_1^2u_1^2p_{11}+ w_1w_2u_1u_2p_{12}\right)+ \left(w_2w_1u_2u_1p_{21}+ w_2^2u_2^2p_{22}\right)$.


Tags 
double, expand, express, products, sum 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Expand and simplify HELP?  yunus27  Math  1  January 1st, 2017 11:27 AM 
How To Expand (a+b+c)(def) Using A Proof...  perfect_world  Elementary Math  8  March 9th, 2016 02:12 AM 
How do I expand this to get this answer?  KaiL  Elementary Math  2  March 7th, 2016 07:55 AM 
Problem with Rewriting Double Sums and Products  w8k17  Elementary Math  2  September 8th, 2014 08:29 PM 
expand the expression  xamdarb  Algebra  2  March 11th, 2014 03:53 PM 