3. [12 marks] Consider a logistic regression model for a binary response y1, . . . ; yn. Let P(x;) = Pr(y: = 1/x;), such that log( 1 - P(x) = x 3. i) [3 marks] Which of the following statement(s) is(are) true? Select ALL the correct statement(s). A. y; and r; follow the Bernoulli distribution with mean P(I;) B. y; follows the Bernoulli distribution with mean P(r;), and a; is nor- mally distributed C. yi follows the Bernoulli distribution with mean P(ri) D. y; follows the Binomial distribution with parameters n and P(x;) ii) [3 marks] Which of the following expression(s) show(s) the log-likelihood log L(B) for the logistic model? Select ALL the correct statement(s). A. IIT, log [P(x ) " (1 - P(x.)) 1-] B. log [EL, P(x )" (1 - P(z,))1 4 ] C. EL -y: log(1 + exp(-x7 8)) - (1 - y:) log(1 + exp(-x; 8)) D. EL, y: log(P(z )) + (1 - y:) log(1 - P(z;)) iii) [3 marks] Which of the following expression (s) show the equation that the MLE of 3 must satisfy? Select ALL the correct statement(s). A. & L(B) = 0 B. log L(B) = 0 C. &L(8) = 0 D. dI a log L(B) = 0