Text: Fundamentals of Probability with Stochastic Processes , by S. Ghahramani
Ch. 1 Axioms of Probability
Required: Ch. 1.1 - 1.4: Sample Space, Events, Axioms of Probability, Basic Theorems
Optional: Ch. 1.5 - 1.7
Ch. 2 Combinatorial Methods
Required: Basic Counting Principles, combinations, permutations (no more than 2 days)
Ch. 3 Conditional Probability and Independence
Required: Ch. 3.1 - 3.5: Conditional Probability, laws of multiplication and total probability, Bayes' Formula, Independence
Optional: Ch. 3.6 Applications of probability to genetics
Ch. 4 Distribution Functions and Discrete Random Variables
Required: Ch. 4.1 - 4.6 Random Variables, distribution functions, discrete random variables, expectation of discrete random variables, variances and moments of discrete random variables, standardized random variables.
Ch. 5 Special Discrete Distributions
Required: Ch. 5.1 - first part of 5.3 Bernoulli and Binomial, Poisson (including Poisson Process), Geometric
Optional: Negative Binomial, hypergeometric
Ch. 6 Continuous Random Variables
Required: Ch. 6.1 - 6.3 Probability density functions, density function of a function of a random variable, expectation and variances
Ch. 7 Special Continuous Distributions
Required: Ch. 7.1 - 7.3 Uniform, Normal , Exponential
Ch. 8 Bivariate Distributions
Required: Ch. 8.1 - 8.3 Joint distributions, independent random variables, conditional distributions
Optional: Ch. 8.4 Transformations of 2 random variables
Ch. 10 More expectations and variances
Required: Ch. 10.1 - 10.4 expected values of sums of random variables, covariance, correlation, conditioning on random variables
Ch. 11 Sums of independent random variables
Required: Ch. 11.1 - 11.3, 11.5 Moment generating functions, sums of independent random variables, Markov and Chebyshev inequalities, Central Limit Theorem
Supplement: Estimators and Confidence Intervals (do as much as possible in no more than 3 days)