My Math Forum Sigma rule question

 March 12th, 2017, 03:57 PM #1 Member   Joined: Jan 2017 From: California Posts: 80 Thanks: 8 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: USA Posts: 1,944 Thanks: 1011 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. Thanks from dthiaw
 March 13th, 2017, 10:03 AM #3 Member   Joined: Jan 2017 From: California Posts: 80 Thanks: 8 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
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Quote:
 Originally Posted by dthiaw yeah but in this case di is definitely not a constant. that is why am surprised
but each individual $d_i$ is.

The summation notation allows for each $d_i$ to be different.

 March 13th, 2017, 10:22 AM #5 Member   Joined: Jan 2017 From: California Posts: 80 Thanks: 8 ok I see what you mean. Thanks a bunch once again

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