final_review - Stat 110 Final Review Fall 2011 Prof Joe Blitzstein 1 General Information The nal will be on Thursday 12\/15 from 2 PM to 5 PM No books

final_review - Stat 110 Final Review Fall 2011 Prof Joe...

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Stat 110 Final Review, Fall 2011 Prof. Joe Blitzstein 1 General Information The final will be on Thursday 12/15, from 2 PM to 5 PM. No books, notes, computers, cell phones, or calculators are allowed, except that you may bring four pages of standard-sized paper (8.5” x 11”) with anything you want written (or typed) on both sides. There will be approximately 8 problems, equally weighted. The material covered will be cumulative since probability is cumulative. To study, I recommend solving lots and lots of practice problems! It’s a good idea to work through as many of the problems on this handout as possible without looking at solutions (and then discussing with others and looking at solutions to check your answers and for any problems where you were really stuck), and to take at least two of the practice finals under timed conditions using only four pages of notes. Carefully going through class notes, homeworks, and handouts (especially this handout and the midterm review handout) is also important, as long as it is done actively (intermixing reading, thinking, solving problems, and asking questions). 2 Topics Combinatorics: multiplication rule, tree diagrams, binomial coe ffi cients, per- mutations and combinations, sampling with/without replacement when order does/doesn’t matter, inclusion-exclusion, story proofs. Basic Probability: sample spaces, events, axioms of probability, equally likely outcomes, inclusion-exclusion, unions, intersections, and complements. Conditional Probability: definition and meaning, writing P ( A 1 \ A 2 \ · · · \ A n ) as a product, Bayes’ Rule, Law of Total Probability, thinking conditionally, prior vs. posterior probability, independence vs. conditional independence. Random Variables: definition and interpretations, stories, discrete vs. contin- uous, distributions, CDFs, PMFs, PDFs, MGFs, functions of a r.v., indicator r.v.s, memorylessness of the Exponential, universality of the Uniform, Poisson approximation, Poisson processes, Beta as conjugate prior for the Binomial. sums (convolutions), location and scale. 1
Expected Value: linearity, fundamental bridge, variance, standard deviation, covariance, correlation, using expectation to prove existence, LOTUS. Conditional Expectation: definition and meaning, taking out what’s known, conditional variance, Adam’s Law (iterated expectation), Eve’s Law. Important Discrete Distributions: Bernoulli, Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson. Important Continuous Distributions: Uniform, Normal, Exponential, Gamma, Beta, Chi-Square, Student- t . Jointly Distributed Random Variables: joint, conditional, and marginal distri- butions, independence, Multinomial, Multivariate Normal, change of variables, order statistics. Convergence: Law of Large Numbers, Central Limit Theorem. Inequalities: Cauchy-Schwarz, Markov, Chebyshev, Jensen.

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