Consider the general non-linear model with known; Yi = m(0, xi) +i. The o minimizes 1(0)...

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Consider the general non-linear model with known; Yi = m(0, xi) +i. The o minimizes 1(0) = n (y - m(0, x)), i=1 and write o to be the true value. (1) (5 pts) Find E l'(00) and El" (00), leaving your answers in terms of the unknown 00. (2) (5 pts) Prove that o El" (00) = Var l'(00). (3) (10 pts) Using the approximation 1' (00) 1'() + (00 ) l" (), which is a first order Taylor expansion, show why we can write 1'(00) C where C = 1" () and is taken to be fixed. (4) (10 pts) Now using the results in part (1) to (3), what would a normal approximation of O be? (5) (10 pts) Hence, construct an approximate (1 a)% confidence interval for 0. Consider the general non-linear model with known; Yi = m(0, xi) +i. The o minimizes 1(0) = n (y - m(0, x)), i=1 and write o to be the true value. (1) (5 pts) Find E l'(00) and El" (00), leaving your answers in terms of the unknown 00. (2) (5 pts) Prove that o El" (00) = Var l'(00). (3) (10 pts) Using the approximation 1' (00) 1'() + (00 ) l" (), which is a first order Taylor expansion, show why we can write 1'(00) C where C = 1" () and is taken to be fixed. (4) (10 pts) Now using the results in part (1) to (3), what would a normal approximation of O be? (5) (10 pts) Hence, construct an approximate (1 a)% confidence interval for 0.