Math 304 final exam Study guide
I Counting; combinations/permutations
Inclusion/Exclusion principle
deMorgan’s laws
Axiomatic definition of probability measure
Equiprobable sample spaces
Bayes’ theorem
Discrete RVs: discrete uniform, Bernoulli, binomial, Poisson, geometric,
hypergeometric
Conditional pmf’s
Expectation; variance
Independence
CDF; derived distribution of a function of one RV
II Continuous RVs: normal, exponential, continuous uniform
Basic properties of normal RVs: using tables
Joint pdfs; marginal pdfs; conditional pdfs
Sums of independent RVs
Expectation, variance of linear combinations of independent RVs
Derived distributions: functions of two random variables
Transformations for pdf of two random variables; Jacobian
Conditional expectation
Covariance; correlation coefficient
Moment Generating Functions
III Limit theorems
Markov; Chebyshev
Central Limit Theorem
IV Markov chains
State transition diagram; transition matrix
regular chains, ergodic chains
absorbing states, transitional states
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