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 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post yunus27 Math 1 January 1st, 2017 11:27 AM perfect_world Elementary Math 8 March 9th, 2016 02:12 AM KaiL Elementary Math 2 March 7th, 2016 07:55 AM w8k17 Elementary Math 2 September 8th, 2014 08:29 PM xamdarb Algebra 2 March 11th, 2014 03:53 PM

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