My question may be a bit too straight forward for this section but I would like to have some incentives here, as I feel like I am missing something. Consider the following simple problem: you give some students a problem to solve. You give a score to this problem which expresses its difficulty. Let's note this difficulty $\delta$. Each student has also a skill score $\lambda$, attached.
The question is the following: how can you accurately estimate the time a student with a particular skill is going to take to solve a problem of a particular difficulty? I have tried to construct a probability distribution based on these two parameters (Weibull) an to randomly select a solving time in this distribution. However it doesnt suit well, as some very low skill students may be able to solve a very difficult problem very fast. It also brings a problem when $\lambda = \delta$.
I am not able to find a reliable solution to this, even if I believe that it should not be so hard. If you have any clue, I would appreciate.
edit: This problem is related to Item Response Theory, I will then investigate here.