sample space

naive definition of probability

counting (multiplication rule, etc .)

sampling

bose einstein

story proofs, eg. vandermonde identity

axioms of probability

birthday problem

properties of probabilty

inclusion - exclusion

matching problem

independence of events

newton peppy's

conditional probability

conditional independence

monty hall problem

simpson's paradox

gambler's ruin, first step analysis

Random variables

CDF's

#PMF's

bernoulli

binomial

Hypergeometric

independence of random variables

geometric

expected values

indicator RV

linearity

symmetry

fundamental bridge

linearity

putnam problem

Negative binomial

St petersburg paradox

sympathetic magic

poisson distribution

popisson approximation

continous RV's ; discrete vs continous

PDF

variance

standard deviation

uniform

universality

standard normal

normal normalizing constant

Normal distribution

standardisation

#LOTUS

exponential distributuopn , memoryless property

Moment generating function

hybrid Baye's rule

Laplace rule of succession

MGF's to get moments of EXpo and normals

sum of possions

joint distrubutions

joint conditional marginal distributions

2D LOTUS

chicken egg problem

expected distance between normals,multinomials,cauchy

covariance

correlation

variance of a sum

variance of hypergeometric

transformations

logNormal

convolutions

the probabilistic method

Beta distribution

baye's billiards

finance preview examples

Gamma distribution

poisson process

Beta- Gamma (post office)

order statistics

conditional expectation

Two envelope paradox

waiting for HT vs HH

taking out whats known

Adams law

eve's Law

Sum of random number of random variables

Inequalities

1. ###Cauchy-Schwarz

2. ###jenson

3. ###markov

4. ###chebyschev

Law of Largne Numbers

Central Limit theorm

Chi- Square

Student-t

Multivariate Normal

Marchov chains

transition matrix

stationary distribution

Irreducibility

reversibility

random walk on an undirected network

Google page rank as Markov chain

Linear regression constants derivation for population