(Monte Carlo) Repeat the Monte Carlo experiment in Exercise 6.1, making each of the following adjustments separately.

(a) Instead of $y_i$, fit $y_i + x_i$ to the explanatory variables 1, $x_i$, and $x_i^{-1}$.

(b) Instead of $y_i$, fit $y_i + x_i x_i$ to the explanatory variables 1 and $x_i^{-1}$.

(c) Generate $x_i$ from a uniform distribution on the interval (9, 10), instead of [1, 10].

Compare the sample means and variances of the fitted coefficients with those from the Monte Carlo experiment in Exercise 8.1. Try to explain your findings.