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.