Download CSE 312 Final Topics and more Slides Probability and Statistics in PDF only on Docsity!
CSE 312 Final Topics
What to bring to the exam ● Calculator, note sheet (8.5”x11”, handwritten or typed, both sides), pencil/pen, eraser, student ID
Study suggestions ● Go through lecture notes, and write down important theorems, definitions, and concepts on note sheet ○ If your class notes aren’t clear, check out course slides or the textbook for alternative explanations (both linked from course web) ○ If you were absent for any lectures, find the lecture notes on the course calendar. ● Do lots of practice problems. Do as many past worksheet problems as you can. ● After studying, test yourself by doing the practice final on the course calendar. ● Ask your peers or the course staff if you’re confused about anything. ○ Post questions on the discussion board under the topic “Final Exam”.
List of topics Counting ● Product rule ● Permutations (order matters) ○ k-permutations ● Combinations (order doesn’t matter) ○ Binomial Theorem ● Understand “with vs. without replacement” (whether repeats are allowed) ● Complementing ● Inclusion-exclusion ● Pigeonhole principle
Probability ● Basic axioms and their corollaries ● Sample space and events ● Equally-likely outcomes ● Independent events ● Conditional probability: definition, chain rule ● Law of Total Probability ● Bayes’ Theorem ● Naïve Bayes Classifier
Discrete random variables and expectation ● Definition of random variable ● Probability mass function ● Expectation ○ Definition ○ E[aX+b] = aE[X]+b, if a and b are constants ○ E[X+Y] = E[X]+E[Y] ○ Indicator random variables ● Independence of random variables ● Variance and standard deviation ○ Definition
○ Var(X) = E[X^2 ] - (E[X])^2 ○ Var(aX + b) = a^2 Var(X), if and b are constants ○ If X & Y independent, Var(X + Y) = Var(X) + Var(Y) ● Important distributions: uniform, Bernoulli, binomial, geometric, Poisson ○ Know what situations they are used for, their probability mass functions, expectations, variances ○ Approximation of binomial random variable by Poisson random variable ○ Application of binomial and Poisson to error-correcting codes
Continuous random variables ● Probability density function ● Cumulative distribution function ● Analogy between discrete and continuous cases (sum vs. integral, PMF vs. PDF, etc.), leading to definitions of expectation and variance ● Important distributions: uniform, exponential, normal ○ Know what situations they are used for, their probability density functions (except for the normal), cumulative distribution functions (Phi table for the normal), expectations, variances ○ Memorylessness of exponential and geometric ● Central Limit Theorem ○ Know versions for both sum and average of i.i.d. samples ○ How to standardize a random variable ○ Continuity correction ○ Approximation of binomial random variable by normal random variable
Tail bounds ● Markov’s inequality ● Chebyshev’s inequality ● Cantelli’s inequality ● Chernoff’s inequality for the binomial distribution
Weak law of large numbers
Maximum likelihood estimators ● Likelihood function ● Know the procedure for finding maximum likelihood estimators ● Maximum likelihood estimators for the two parameters of the normal distribution ● Bias ● Confidence intervals
Probabilistic algorithm ● Quicksort ● Freivalds’ algorithm for verifying matrix multiplication ● Karger’s min cut algorithm
