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Calculus & Analysis

Foundations

Overview
Sample Space & Events
Probability Axioms
Counting
Conditional Probability
Bayes Theorem
Independence
Problems V1
Come Later

Random Variables

introduction
Discrete random variables
Continuous random variables
Cumulative distribution functions
Random vectors
Functions of random variables

Expectations and Moments

Expected value
Variance standard deviation
Moments
Covariance correlation
Covariance matrix
Conditional expectation

Common Distributions

Overview
Discrete distributions
Binmoial Distribution
Multinomial distribution
Bernoulli binomial
Poisson distribution
Geometric negative binomial
Continuous distributions
Uniform exponential
Normal distribution
Gamma beta distributions
Multivariate normal

Independence and Joint Distributions

Joint distributions
Marginal distributions
Conditional distributions
Independence random variables
Sums independent rvs
Convolutions

Transformations

Transformation technique
Jacobian method
Mgf characteristic functions
Joint mgf
Cumulant generating function

Limit Theorems and Inequalities

Markov inequality
Chebyshev inequality
Jensen inequality
Law large numbers
Central limit theorem
Convergence concepts

Advanced Topics

Order statistics
Quantiles
Indicator functions
Kullback leibler divergence
Zero probability events
Rigorous conditional probability

Foundations

Conditional Probability

What is conditional probability
Low ot Total Probabiility

P(A | B) = P(A ∩ B) / P(B)

Counting Bayes Theorem

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