Suppose there are $n$ mutually uncorrelated assets. The return on asset $i$ has variance $\sigma_{i}^{2}$. The expected rates of return are unspecified at this point. The total amount of asset $i$ in the market is $X_{i}$. We let $T=\sum_{i=1}^{n} X_{i}$ and then set $x_{i}=X_{i} / T$, for $i=1,2, \ldots, n$. Hence the market portfolio in normalized form is $\mathbf{x}=\left(x_{1}, x_{2}, \ldots, x_{n}\right)$. Assume there is a risk-free asset with rate of return $r_{f}$. Find an expression for $\beta_{j}$ in terms of the $x_{i}$ 's and $\sigma_{i}$ 's.