So we have these random variables A,B,C where A and B are 2 independent uniform distribution variables both with I=[$\frac {-1} {2}$,$\frac {1} {2}$]
$C=A+B$
We have to find the correlation coefficient $\rho_{AC}$
From what i know and have done so far $\rho_{AC}$=$\frac {\sigma_{AC}} {\sigma_A*\sigma_c}$
From what i did(hopefully i did it right):
Even though independent A and B basically have the same Variance So $\sigma_{A}=\sigma_{B}=$$\frac {1} {12}$
What i dont know how to do is how to figure out the $\sigma_{AC}$
From what i know: $\sigma_{AC}=$E[AC]-$\mu_A\mu_C$
$\mu_A=0$ and $\mu_c=0$ since C=A+B and A and B are independent we can find $\mu_C=\mu_A+\mu_B$ and since $\mu_A=\mu_B=0$ $\mu_C=0$
So $\sigma_{AC}=E[AC]$
And this is where im stuck. I dont know how to calculate $E[AC]$