Question: Maximizing a Quadratic Response. Consider the model, Yi = flo + fl1Xi + fl2XT + ei, eiS Li.d. N(O, a2), i = 1,2,3, ... ,

Maximizing a Quadratic Response.

Consider the model, Yi = flo + fl1Xi + fl2XT + ei, eiS Li.d. N(O, a2), i =

1,2,3, ... , n. Let Xo be the value at which the function E(y) = flo + fl1X +

fl2X2 is maximized (or minimized).

(a) Find the maximum likelihood estimate of Xo.

(b) Find a (1 - 0:)100% confidence interval for Xo. Does such an interval always exist?

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