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

[Roni1985]

Homework Statement

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

Homework Equations

The Attempt at a Solution

Why can't I do this?:
E[X₁+X₂+...+X_n]=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?

 

[LCKurtz]

You can do that. The expected value operator is linear.

 

[Roni1985]

You can do that. The expected value operator is linear.

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

Thanks.