A course lecturer, who teaches a whole$-$year course, CS$101,$ at a university in the UK$,$ needs to find a way to determine pass$/$fail grade for each student in the class without having marks for the final examination that was cancelled due to a worldwide pandemic. Apart from the final examination, which was cancelled, the course has five assignments, for which marking has been done already. As a first attempt, the lecturer employed a logistic regression model that takes an input vector $x=(x_1,x_2,$dots,$x_5),$ where $x_i,1i5,$ represents the marks of $i-$th assignment. Using the course data of around $500$ students for the last two years, the lecturer trained the model and obtained classification accuracy $($ACC$)$ of $0\mathrm{.}95.$

$($a$)$ Write out the form of a logistic regression model for this task, clarifying what variables you use, and explain how you decide pass$/$fail with the model given $x.$

$($b$)$ Within the last two years data, the lecturer wanted to avoid the case that students who passed the course were predicted as 'fail' by the classifier. Explain how this could be achieved without retraining the model and discuss its possible side effects.

$($c$)$ After some parameter tuning, the lecturer confirmed the classifier predicted pass$/$fail grades satisfactory. Discuss possible problems with using the clas$-$

marks$]$

sifier to predict pass$/$fail grades for this year.