Probability= sum of n uniformly distributed r.v.'s

Roni1985
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Homework Statement


Xi ~ U(80,120)
find the E[X1+X2+...+Xn]=?

Homework Equations





The Attempt at a Solution



Why can't I do this?:
E[X1+X2+...+Xn]=n*E[X1]
and just find the expected value?

Is that because the distribution changes as we increase the number of elements of uniforms we sum?
Is there some trick here?

I found something called "Irwin–Hall distribution"... is this it?
 
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You can do that. The expected value operator is linear.
 
LCKurtz said:
You can do that. The expected value operator is linear.

I see, I guess the fact that the distribution changes, confused me...

Thanks.
 
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