Question

Rule of Means:

Proper Notation shown below:

Answer 1

\[\mu_{x-y} = \mu_{y-x}?\]
I came across this question. I'm pretty sure it's not but I just want to make sure

Answer 2

What is the context?

Answer 3

Context doesn't matter, it's just the general rule.

Answer 4

I don't understand.. are you talking about probability distributions (gaussian?) ?
You should define what is \(\mu_a\) .. for some \(a\)..

Answer 5

I suck at stats but does this help you at all

http://www.kaspercpa.com/statisticalreview.htm

Answer 6

I checked that website actually. It stated that E(X+Y) = E(X) + E(Y), didn't say anything about E(X-Y) though so I guess they thought it would be E(X) - E(Y)

Okay sorry about the context. It's for a simple probability distribution.

Answer 7

honestly I have no idea about stats but
E(X-Y)=E(X+(-Y)
let Z=-Y
E(X+Z)=E(X)+E(Z)
so E(X+Z)=E(X)+E(-Y)
and E(aX)=aE(X)
so
E(-Y)=-1E(Y)

so
E(X-Y)=E(X)-E(Y)

am I wrong??

Answer 8

@mhchen

Answer 9

@amorfide Your development is correct.

Out of the blue, I would say: rule of means is wrong
the rule with the sigma's is correct. (variance does not suffer from a negative sign)

Answer 10

Yeah I got it.

You proved E(X-Y) = E(X) - (Y)

So based on that
E(X-Y) does NOT equal to E(Y-X)

Answer 11

E(X-Y)=E(-(Y-X))
let Z=Y-X
E(-Z)=-E(Z)
hence
E(X-Y)=-E(Y-X) I think

Answer 12

yep.