>>15926367 There's no category theory here. It's just a discrete random variable with k possible states and specified respective probabilities.

The KL divergence thing is a bit different and somewhat outside of standard statistics (really it's an information theory thing that statisticians borrow for hypothesis testing information bounds).

>>15926364 >probability and statistics are what made me give up biotechnology studies and put my life on the track of 15 years incel failure, and counting.

>>15926374 Yes, the word categorical is used, that doesn't mean you need category theory to describe the random variable.

It just means that the random variable is in one of k states. You could think of this like corresponding to being associated to a unit vector in one of k directions in R^k. You don't need category theory for this.

You need, at most, some linear algebra, a bit of experience with series simplifications, and some patience.

>>15926413 The geometric series does actually have something to do with geometry believe it or not.

If you take any three consecutive terms in a geometric series, the one in the middle is the geometric mean of the two on either side of it. Meaning, the middle term is the side-length of a square whose total area is given by the product of the two terms on either end.

>>15928711 >>15928707 A really good resource for undergrad to early grad level probability is Bertsekas's Introduction to Probability.

It's super easy to find a PDF of the book as well as the associated MIT courseware and doesn't ask much of students in terms of prerequisites except for a familiarity with some multivariable calculus and a little bit of linear algebra towards the end.

I remember an anon asked me to make a infographic on the whole "how do I start with probability" thing and I was working on it and got a bit sidetracked. I'm less busy between semesters so I can try to put something together.

>>15926379 How do series make an appearance in probability, besides the usual gimmick of approximating difficult to integrate functions via power series

>>15928809 A partial geometric series describes the probability of waiting x \leq k trials before the first successful trial of a binary/Bernoulli random variable of probability p (as an example).

Infinite series give you the way of calculating probabilities and expectations of (countable) infinite length random variables.

>>15928787 PhD in EE with a concentration in adaptive statistical estimation/detection. My job is basically just probability and stochastic processes but for statistical signal processing applications.

>>15928720 >I remember an anon asked me to make a infographic on the whole "how do I start with probability" thing and I was working on it and got a bit sidetracked. I'm less busy between semesters so I can try to put something together. Based. Any recommendations for now as far as math foundations?

>>15929666 If you want to do probability/statistics at an undergraduate STEM major level, you need to be pretty comfortable with multivariable calculus, ordinary differential equations/Fourier/Laplace transforms (for moment generating functions/characteristic functions) and linear algebra (for linear estimation).

If you aren't comfortable with those, that's where you want to start. Some discrete mathematics for infinite series will also be very helpful.

>>15926364 Probability and statistics are only limited to a single closed dataset and have a very niche application, for the entire universe as a system they are useless and the probability of anything happening at any given moment is 50/50

>>15929882 Would you say that Hubbard & Hubbard: Vector Calculus, Linear Algebra and Differential Forms is sufficient for a one-stop math undergrad? And then pursue with probability?

>>15930143 Linear Algebra and vector calc are a lot more important in statistics than probability.

I'm not familiar with the book you've linked, but if you can handle convolution integrals, Laplace/Fourier transforms, some basics of combinatorics and changes of variables, you've got pretty much everything you need for a basic undergraduate probability course.

The only way to know for certain is to give some problems a try.