Consider an economy with a risk free asset with return \(r_{f}\) and \(N\) risky assets with i.i.d. random returns \(\tilde{\mathbf{r}}=\left(\tilde{r}_{1}, \ldots, \tilde{r}_{N}\right)\). Show that the two mutual funds separation property holds with respect to the risk free asset and the equally weighted portfolio \((1 / N, \ldots, 1 / N)^{\top}\) of the risky assets.