Asking for inspiration I am a teacher. I want to create a system where my students will take exams online and I will predict their chances of getting a certain marks in the final exam.
Is there any mathematical model where I can take inspiration from?
 A: If you are just at the stage of proposing a system, you needn't worry too much about which statistically model is likely to model the marks well.  What is far more important is to make plan a consistent assessment scheme and collect data.  If you have a large amount of past data, and reasonable consistency of assessment over time, you will probably find you can build a reasonable predictive model.  If you don't have much data, or if the structure of the data changes regularly, it will be a struggle.
Once you get to the stage where you have a reasonable amount of data, it would be likely that you will want to employ some kind of regression model, with the goal of predicting the outcome of a new assessment from outcomes in past assessments.  If you want to to get a predictive distribution over the full range of allowable marks (as opposed to just predicting categories of outcome) then a good place to start would be a GLM with an outcome over a fixed interval range.  Ultimately, the appropriate model will depend on your data, so it is not possible to tell you which model is appropriate prior to seeing some data.
