expected value for squared sum of uniform distribution

204 Views Asked by At

$X_1,...,X_n$ are i.i.d distributed with $X_1 \sim U(0,\theta), \theta > 0$, how does one get the expected value for $Y = (\sum X_i)^2$? For those types of questions I normally use the linearity of the expected value, especially $E(XY) = EXEY$ if the expected values are independend, but $X_i$ is not independend from $X_i$ thats why I can't use it here right?