Probability — Study Path Agent

Chapter 1

Foundations & Probability Axioms

1

Sample spaces, events, set operations

2

Kolmogorov axioms, probability measures

3

Venn diagram reasoning + practice problems

Chapter 2

Counting & Combinatorics for Probability

4

Basic counting rules (product/sum rules)

5

Permutations & combinations

6

Multinomial coefficients

7

Counting practice: cards, dice, strings, anagrams

Chapter 3

Random Variables & Distributions (Core)

8

Discrete random variables: pmf, cdf

9

Continuous random variables: pdf, cdf

10

Bernoulli & Binomial distributions

11

Geometric & Negative Binomial distributions

12

Poisson distribution & Poisson process intuition

13

Uniform, Exponential, Normal distributions

14

Distribution fitting + sanity checks (mean/variance)

Chapter 4

Expectation, Variance & Transforms

15

Expected value as a sum/integral

16

Variance, standard deviation, covariance

17

Linearity of expectation (problem techniques)

Chapter 5

Conditional Probability & Bayesian Thinking

18

Conditional probability & independence

19

Bayes' theorem + posterior updating drills

20

Common Bayesian models: Beta-Binomial, Gamma-Poisson (conceptual)

21

Naive Bayes classification (probability viewpoint)

Chapter 6

Limit Theorems & Convergence

22

Modes of convergence (in probability, a.s., in distribution)

23

Law of Large Numbers (LLN) + examples

24

Central Limit Theorem (CLT) + normal approximations

25

Sums of independent random variables (convolution basics)

26

Monte Carlo simulation to validate LLN/CLT (hands-on)