$4.($Wild cats$)$ Suppose there are n assets which are uncorrelated. $($They might be n different $$wild cat$$ oil well prospects.$)$ You may invest in any one, or in any combination of them. The mean rate of return $$r is the same for each asset, but the variances are different: the return of asset i has a variance of $2$ i for i $=1,2,...,$ n$.$ Denote $2=$ Xn i$=11$ $2$ i $!1.$ Find the global minimum$-$variance portfolio and its variance $($express your results in terms of $2$ i $,$ i $=1,,$ n$,$ $2,$ and $$r$,$ but not all of them are necessarily used$).$