PROBABILITY (DARTMOUTH COLLEGE, 2014)

LECTURE SLIDES

WEEK 1 - Basic concepts:

discrete probability,

introduction to probability distributions,

infinity and introduction to continuous probabilities,

WEEK 2 - Combinatorics

cumulative distibutions, permutations,

counting combinations,

binomial distribution and inclusion-exclusion,

WEEK 3 - Conditional Probability

discrete conditional probability,

continuous conditional probability + worksheet with solutions

Poisson distribution (and others),

WEEK 4 -

functions of random variables,

normal density,

review for the midterm + mock midterm with solutions.

WEEK 5 - Expected Value, Standard Deviation and Variance

expected value.

variance, coupon collector's problem,

sums of independent random variables,

WEEK 6 - Law of Large Numbers and Central Limit Theorem

Law of Large Numbers + solutions.

Central Limit Theorem: first glance,

Central Limit Theorem: applications,

WEEK 7 - Joint Distributions

puzzles,

,

joint distributions.

WEEK 8 - Markov Chains

random walks,

Markov chains, stationary distribution,

absorbin Markov chains, matrix methods.

WEEK 9 - Markov Chains - continued

hitting times, irreducible and reversible Markov chains,

Markov chains practice,

Markov Chain Monte Carlo.

ASSIGNMENTS

Python primer + exercises

week 1

week 2

week 3

week 4

week 5

week 6

week 7

week 8 + 9