Suppose there are n mutually uncorrelated assets. The return of asset i has variance of 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=summation^n_i=1 X_i and then set x_i = X_i/T, for i = l,2...n. Hence the market portfolio in normalized form is x = (x_1,x_2..x_n). 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