2. [50 points} Consider the logistic regression. 'We observe (Xi, K}, i = 1, . . . , n, where X:- E R\" and Y; E {1,1}. \"We draw X:- from a normal distribution Man\") and assume [3" = {1} V9, .. .11} V9] Given Xi and :3, we draw 1'; from the following Bernoulli distribution Consider using gradient descent to nd the maximum likelihood estimator of this model. [a] Implement gradient descent method with the initial point 5W} 2 (, . . . ,} and the backtracking line search. Please use R or Python to implement it from the scratch and you need to submit your R or Python script. [13] Draw plots of convergence rate when n = 2,d = 5 and n = , d = 5. In each plot, the r-axis is the number of step Ill: and y-axis is log \