If a student has ability \(a\), and a probably is \(d\) difficulty, the probability of a student getting something right:

\begin{equation} \sigma (a-d) \end{equation}

this doesn’t consider SLIPPING at all.

https://en.wikipedia.org/wiki/It%C3%B4%27s_lemma

for integrating Differential Equations with Brownian Motion.

https://fhir-ehr-code.cerner.com/r4/ec2458f2-1e24-41c8-b71b-0e701af7583d/.well-known/smart-configuration

for random variables \(X, Y\), the joint probability distribution is the probability of both of them happening at once.

\begin{equation} p(x,y) \end{equation}

The most fundamental solution can be derived with a table where all complete probabilities are listed. They are going to be too large to practically store.

independent joint probability

For any given variable, the probability of the joint of two separate events is their product.

probability of the joint of a Bayes Net

\begin{equation} p(joint) = \prod_{i \in BN}^{} p(x_{i} | parents(x_{i})) \end{equation}