These are multiple choice questions, can you please select ALL the correct statements (i.e there might be more than one correct answer). It would be helpful if you could also briefly explain why you selected those answers. Please do all the parts if possible (since they are just multipel choice questions. Thank you in advance.

Consider a logistic regression model for a binary response y1, . . . , yn. Let P(r.) = Pr(yi = 1/r;), such that P(I.) log ]- P(I.) = I; B. Which of the following statement(s) is(are) true? Select ALL the correct statement(s). A. y; and I; follow the Bernoulli distribution with mean P(r;) B. y; follows the Bernoulli distribution with mean P(r;), and r, is nor- mally distributed C. y; follows the Bernoulli distribution with mean P(I;) D. y; follows the Binomial distribution with parameters n and P(r;) ii) 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. II, log [P(r.) (1 - P(r;)) 1-w B. log [), P(I,)" (1 - P(r;)) 1-y.] C. EMI -y: log(1 + exp(-I, B)) - (1 - y;) log(1 + exp(-I; B)) D. EL, y: log(P(r,)) + (1 - y;) log(1 - P(r;)) 111 Which of the following expression(s) show the equation that the MLE of 8 must satisfy? Select ALL the correct statement(s). A. &L(B) =0 B. To log L(B) = 0 C. DEL(B) = 0 D. & log L(8) = 0 iv) Let B, be the MLE of 8 for the model with y as response, the maximum likelihood estimator By satisfies exp(-I, By) 1 + exp(-IT By) Let Let 2; =1-yi, so that z, is one when y; is zero and vice versa. Let , denote the MLE of 8 for the model with = as response. Which of the fol- lowing expression(s) are correct? Select ALL the correct statement(s). A. E.an = E.I Itexp(=] 8,) B. E. & = ).I; Itexp(=] By) C. Ear = EI( exp(17 82 ) 1+exp(3 8) D. Can = EI, ( 1+exp(-= P.)