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The mean of a sum of variables.by Mppl
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#1
Nov411, 03:38 PM

P: 13

How do I prove that the mean of a random variable Z which is the sum of to other random variables X and Y is the sum of the mean of X with the mean of Y?



#2
Nov411, 03:48 PM

Sci Advisor
P: 6,077

Essentially the theorem is equivalent to the theorem that the integral of a sum is the sum of the integrals.



#3
Nov411, 03:54 PM

P: 13

well I obviously know that the integral of the sum is the sum of the integral but I don't know how I can relate that to the situation a mentioned, can you please be more specific?
I'm trying to prove it and I'm getting a convultion integral so far... thank you. 


#4
Nov411, 09:58 PM

P: 523

The mean of a sum of variables.
Another approach that would work for the nonindependent case is to consider separately the joint distribution and marginal distributions of X and Y. 


#5
Nov511, 04:06 AM

P: 13

well but I'm not being able to prove it either for dependent or independent variables, can you please show me the proof or tell me where I can find it? thank you



#6
Nov511, 04:03 PM

Sci Advisor
P: 6,077

Two random variables.
E(X+Y)=∫∫(x+y)dF(x,y)=∫∫xdF(x,y) + ∫∫ydF(x,y). Integrate with respect to y in the first integral and integrate with respect to x in the second integral. You will be left with E(X) + E(Y). In the above F(x,y) is the joint distribution function. 


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