arXiv subjects
Publications and source records attributed to Benjamin Otto.
We use learning data of an e-assessment platform for an introductory mathematical statistics course to predict the probability of passing the final exam for each student. Subsequently, we send warning emails to students with a low predicted probability to pass the exam. We detect a positive but imprecisely estimated effect of this treatment, suggesting the effectiveness of such interventions only when administered more intensively.
We analyze learning data of an e-assessment platform for an introductory mathematical statistics course, more specifically the time of the day when students learn. We propose statistical models to predict students' success and to describe their behavior with a special focus on the following aspects. First, we find that learning during daytime and not at nighttime is a relevant variable for predicting success in final exams. Second, we observe that good and very good students tend to learn in the afternoon, while some students who failed our course were more likely to study at night but not successfully so. Third, we discuss the average time spent on exercises. Regarding this, students who participated in an exam spent more time doing exercises than students who dropped the course before.
The primary goal of this document is to record the asymptotic effects that preimage constraints impose upon the sizes of the iterated images of a random function. Specifically, given a subset $\mathcal{P}\subseteq \mathbb{Z}_{\geq 0}$ and a finite set $S$ of size $n$, choose a function uniformly from the set of functions $f:S\rightarrow S$ that satisfy the condition that $|f^{-1}(x)|\in\mathcal{P}$ for each $x\in S$, and ask what $|f^k(S)|$ looks like as $n$ goes to infinity. The robust theory of singularity analysis allows one to completely answer this question if one accepts that $0\in\mathcal{P}$, that $\mathcal{P}$ contains an element bigger than 1, and that $\gcd(\mathcal{P})=1$; only the third of these conditions is a meaningful restriction. The secondary goal of this paper is to record much of the background necessary to achieve the primary goal.