(Solved): [10 marks] 5. Suppose that we are fitting the straight line Y_i=\beta _0+\beta _1 x_i+_i, but the ...

[10 marks] 5. Suppose that we are fitting the straight line Y_i=\beta _0+\beta _1 x_i+ϵ_i, but the variance of the Y_i 's now depend on the level of x; that is, V(Y_1| x_1)=\sigma ^2/w_1, V(Y_2| x_2)=\sigma ^2/w_2, ⋯, V(Y_n| x_n)=\sigma ^2/w_n where the w_i are known constants, often called weights. Find the maximum likelihood estimates for \beta _0 and \beta _1. Assume that E(ϵ_i)=0 and that Y 's are Normally distributed. Show all your work and circle your final answers.