How can we find the value of the following term,
$ E[\prod_{i = 1}^{L}{\sum_{j = 1}^{K}{a_{ij}}}] $
i.e., the expected value of the product of the sum of $a_{ij}$'s where $a_{ij}$ is a random variable drawn from a probability distribution $f(x)$. How can I compute the value for a general $f(.)$? What if $f(x) = \frac{1}{\sqrt{x}}$ and $c_1 \le x \le c_2$?