3. (Simulation Exercise) Consider the linear regression model Yn = x² + nn 0 where 0 € R². Generate the coefficients of the unknown vector 0, randomly according to the normalized Gaussian distribution, N(0, 1). The noise is assumed to be white Gaussian with variance 0.1. The samples of the input vector are i.i.d. generated via the normalized Gaussian. Apply the following Robbins-Monro algorithm On = On-1+ Hnxn (yn - x0n-1) for the optimal MSE linear estimation with a step size equal to n = 1/n. Run 1000 independent experiments and plot the mean value of the first coefficient of the 1000 produced estimates, at each iteration step. Also, plot the horizontal line crossing the true value of the first coefficient of the unknown vector. Furthermore, plot the standard deviation of the obtained estimate, every 30 iteration steps. Comment on the results. Play with different rules of diminishing step sizes and comment on the results.

Fig: 1