Part 3Math for LLMs

Introduction and Random Variables: Part 3 - Appendix R Notation Reference For Chapter 6

Probability Theory / Introduction and Random Variables

OverviewLesson map Part 1Intuition To 12 Exercises Part 2Why This Matters For Ai 2026 Perspective To Appendix Q Historical D Part 3Appendix R Notation Reference For Chapter 6 Theory NotebookRunnable lab Exercises NotebookPractice lab

Private notes

0/8000

Notes stay private to your browser until account sync is configured.

Part 3

3 min read7 headingsSplit lesson page

Lesson overview | Previous part | Lesson overview

Introduction to Probability and Random Variables: Appendix R: Notation Reference for Chapter 6

Appendix R: Notation Reference for Chapter 6

This reference card collects all notation used in this chapter. Consistent notation prevents ambiguity when working across sections.

R.1 Sets and Events

Symbol	Meaning
$\Omega$	Sample space
$\omega \in \Omega$	Elementary outcome
$A, B, C$	Events (subsets of $\Omega$ )
$A^c$	Complement of $A$
$A \cap B$	Intersection (both $A$ and $B$ )
$A \cup B$	Union (either $A$ or $B$ )
$A \setminus B$	Set difference ( $A$ but not $B$ )
$A \triangle B$	Symmetric difference
$\mathbf{1}_A$ or $\mathbf{1}[A]$	Indicator function of event $A$
$\mathcal{F}$	Sigma-algebra of events

R.2 Probability

Symbol	Meaning
$P(A)$	Probability of event $A$
$P(A \\| B)$	Conditional probability of $A$ given $B$
$P(A, B)$	Joint probability $P(A \cap B)$
$A \perp B$	Events $A$ and $B$ are independent

R.3 Random Variables

Symbol	Meaning
$X, Y, Z$	Random variables
$x, y, z$	Values (realisations) of random variables
$F_X(x)$	CDF of $X$ : $P(X \leq x)$
$f_X(x)$	PDF of $X$ (continuous)
$p_X(x)$	PMF of $X$ (discrete)
$\text{supp}(X)$	Support: $\{x : p_X(x) > 0\}$ or $\{x : f_X(x) > 0\}$
$X \sim p$	$X$ has distribution $p$
$X \perp Y$	$X$ and $Y$ are independent random variables
$X \perp Y \\| Z$	$X$ and $Y$ are conditionally independent given $Z$

R.4 Named Distributions

Notation	Distribution
$X \sim \text{Bernoulli}(p)$	Bernoulli with success probability $p$
$X \sim \text{Binomial}(n, p)$	Binomial: $n$ trials, success probability $p$
$X \sim \text{Geometric}(p)$	Geometric: trials until first success
$X \sim \text{Poisson}(\lambda)$	Poisson with rate $\lambda$
$X \sim \text{Uniform}(a, b)$	Uniform on interval $[a,b]$
$X \sim \mathcal{N}(\mu, \sigma^2)$	Gaussian with mean $\mu$ and variance $\sigma^2$
$X \sim \text{Exponential}(\lambda)$	Exponential with rate $\lambda$
$Z \sim \mathcal{N}(0,1)$	Standard normal
$\Phi(z)$	CDF of the standard normal

R.5 Expectation and Moments

Symbol	Meaning
$\mathbb{E}[X]$	Expected value of $X$
$\mathbb{E}[X \\| Y]$	Conditional expectation of $X$ given $Y$
$\mu_X$	Mean of $X$ ( $= \mathbb{E}[X]$ )
$\sigma^2_X$ or $\text{Var}(X)$	Variance of $X$
$\sigma_X$	Standard deviation of $X$
$\text{Cov}(X,Y)$	Covariance of $X$ and $Y$
$\rho_{XY}$	Pearson correlation
$M_X(t)$	Moment generating function
$G_X(z)$	Probability generating function
$\varphi_X(t)$	Characteristic function

R.6 Information Theory

Symbol	Meaning
$H(X)$	Shannon entropy of $X$
$H(X, Y)$	Joint entropy
$H(X \\| Y)$	Conditional entropy
$I(X; Y)$	Mutual information
$D_{\mathrm{KL}}(p \\| q)$	KL divergence from $q$ to $p$
$H(p, q)$	Cross-entropy of $q$ under $p$

End of Appendices. Return to Table of Contents.

Skill Check

Test this lesson

Answer 4 quick questions to lock in the lesson and feed your adaptive practice queue.

--

Score

0/4

Answered

Not attempted

Status

1

Which module does this lesson belong to?

2

Which section is covered in this lesson content?

3

Which term is most central to this lesson?

4

What is the best way to use this lesson for real learning?

Your answers save locally first, then sync when account storage is available.

Previous lesson Next lesson