## Notation

### shorthand for probability

Take

\begin{equation} P(X = 1) = \frac{1}{6} \end{equation}

We can write this in short hand like:

\begin{equation} P(X^{1}) = P(X=1) = \frac{1}{6} \end{equation}

### \(P\) vs \(p\)

Upper case \(P\) for probability mass function (one shot chance), lower case \(p\) for probability density functions (integral)

## New Concepts

- degrees of belief and describing them using the language of probability
- discrete distribution and continuous distribution and joint probability distribution
- fun probability distributions
- conditional probability and Bayes Theorem
- unique models that leverage conditional probability
- conditional Gaussian models
- linear gaussian model
- conditional linear Gaussian models: use your big brain to add up 1) and 2), with continuous random variables \(X, Y\), and a discrete \(Z\), where \(p(x \mid y, z)\).
- sigmoid model

- unique models that leverage conditional probability
- Baysian Network and conditional independence

## Important Results / Claims

- history and impact of decision making
- law of total probability
- fun axioms
- belief axioms:
- probability axioms:

- Methods of Compressing the Parameters of a Distribution
- assuming independence
- using a decision tree

- checking for conditional independence