What is the first and second and third derivative with respect to $w_{i}$ of the following function ?? ($r_{i}$'s are random variables) $$f(w,r)=E\bigg[\bigg(\sum_{i=1}^{n}{w_{i}(a-r_{i})},0\bigg)_{+}^3 \bigg]$$
I am getting the answer: $\frac{\partial f}{\partial w_{i}}=3E\bigg[\bigg(\sum_{i=1}^{n}{w_{i}(a-r_{i})},0\bigg)^2_{+} (a-r_{i})\bigg]$
and $\frac{\partial^2 f}{\partial w_{i}^2}=6E\bigg[\bigg(\sum_{i=1}^{n}{w_{i}(a-r_{i})},0\bigg)_{+} (a-r_{i})^2\bigg].$
Also what would be the third derivative ?
I am not sure about the answers. please clarify me.