5. Third-degree Burns. The data for this exercise, discussed in Fan et al. (1995), refer to 'n, : 435 adults who were treated for third-degree burns by the University of Southern California General Hospital Burn Center. The patients were grouped according to the area of third-degree burns on the body. For each midpoint of the groupings \"log(area 41),\" the number of patients in the corresponding group who survived and the number who died from the burns was recorded: Log(area+1) Survived Died 1.35 13 0 1.60 19 0 1.75 67 2 1.85 45 5 1.95 71 8 2.05 50 20 2.15 35 31 2.25 7 49 2.35 1 12 (a) Fit the logistic regression on the probability of death due to thirddegree burns with the covariate x = log(area+1). What is the deviance? (b) Using your model, estimate nd the posterior probability of survival for a person for which log(area + 1) equals 2