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March 12th, 2017, 03:57 PM  #1 
Member Joined: Jan 2017 From: California Posts: 64 Thanks: 5  Sigma rule question
Hi everyone I was wondering why this equality is true considering that $d_i$ is not a constant $\sum E(d_{i}u_{i})=\sum d_{i}E(u_{i})$ $\[d_{i}=(x_{i}\bar{x})\]$ Thank you in advance Last edited by dthiaw; March 12th, 2017 at 04:03 PM. 
March 12th, 2017, 10:09 PM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,238 Thanks: 637 
if $d_i$ is a constant then for any random variable $u_i$ $E[d_i u_i] = d_i E[u_i]$ It's not clear whether $d_i$ is a rv or not. 
March 13th, 2017, 10:03 AM  #3 
Member Joined: Jan 2017 From: California Posts: 64 Thanks: 5 
yeah but in this case di is definitely not a constant. that is why am surprised Last edited by dthiaw; March 13th, 2017 at 10:06 AM. 
March 13th, 2017, 10:16 AM  #4 
Senior Member Joined: Sep 2015 From: CA Posts: 1,238 Thanks: 637  
March 13th, 2017, 10:22 AM  #5 
Member Joined: Jan 2017 From: California Posts: 64 Thanks: 5 
ok I see what you mean. Thanks a bunch once again


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