I have been teaching a course on stochastic processes to master students in theoretical physics, and half of my students seem to have never taken a probability course and struggle with some basic concepts such as conditional probability, conditional expected value, and conditional variance. They're physicists, so they have seen a lot of probabilistic calculations in quantum mechanics and statistical physics, they know mean and variance, and have used probability density functions.
I did not want to teach them a basic probability lecture because of time constraints and not wanting to lose more advanced students. And also because I absolutely do not need a formal definition of probability involving measures.
They usually do fine with half of the course, but when I start writing things like$$\text{Var}(X) = \left\langle\text{Var}(X|Y) \right\rangle + \text{Var}(\left\langle X|Y\right\rangle),$$I lose most of the students.
What I'm looking for: I am looking for a good reference (short book chapter, lecture notes, video lectures + a problem set) to give a one to two-hour lecture on conditional probability, conditional expected value, conditional variance, and some review of maybe more basic stuff. Something that is not too formal (no measure theory, no formal proofs) and is suitable for master students in theoretical physics who have seen some probability but need a refresher on the more advanced stuff.
I know I can write this myself, but it feels like reinventing the wheel, as no doubt, many other lecturers have faced this problem teaching in physics, and by now have perfected the way to do this.
