Aug 25: Introduction to the course, Relative frequency, Deterministic and probabilistic models (Sec 1.2 and 1.3), Examples (Sec 1.5) Aug 27: Statistical regularity, relative frequency (Sec 1.3), Discrete and continuous sample spaces (Sec 2.1), Axioms of probability (Sec 2.2) Aug 28: Results based on axioms of probability (Sec 2.2), random number generators (Sec 2.7) Sep 03: Probability law assignment in discrete and continuous sample spaces (Sec 2.3) Sep 04: Counting methodes: Sampling with replacement and with ordering, Sampling without replacement and with ordering, Sampling without replacement and without ordering, Sampling with replacement and without ordering (Sec 2.3). Sep 08: Conditional probability, Theorem of total probability, Bayes's rule (Sec 2.4) Sep 10: Independence of events (Sec 2.5) Sep 11: Sequential experiments, Sequence of independent experiments, Binomial law, (Sec 2.6) Sep 15: Sequence of independent events: Multinomial law, Geometric law; Sequence of depenent events (Sec 2.6) Sep 17: Sample statistics (mean, median, mode, variance, standard deviation), Introduction to random variables (Sec 3.1) Sep 18: Cumulative Distribution Function, properties of CDF, probability mass function (Sec 3.2) Sep 22: Probability density function, properties of pdfs (Sec 3.3) Sep 24: (Fire drill) Conditional pdfs and CDFs (Sec 3.3), Bernoulli and Binomial random variables (Sec 3.4) Sep 25: Sec 3.4: Geometric random variable, memoryless propery, Poisson random variable (Sec 3.4) Sep 29: Poisson distribution, its approximation to the Binomial distribution, Continuous distributions: uniform and exponential (Sec 3.4) Oct 01: Memoryless property of exponential distribution, Gaussian random variable, change of variables, Q and phi functions (Sec 3.4) Oct 02: Gamma random variable (Sec 3.4), Introduction to functions of random variables, Dicrete functions of random variables (Sec 3.5) Oct 06: Functions of random variables: finding the pdf directly (Sec 3.5) Oct 08: Functions of random variables: a general method (Sec 3.5) Oct 09: Expected value of a random variable, Properties of the expected value (Sec 3.6) Oct 14: Expectation of functions of random variable, Second moment and variance of a random variable (Sec 3.6) Oct 15: Markov and Chebyshev inequalities (Sec 3.7), Transform Methods (Sec 3.9) Oct 16: Methods to generate random numbers (Sec 3.11), Exam review 10-20 MIDTERM 10-22 Chi-square [3.8] 10-23 Chi-square test (cont'd) 10-27 reliability [3.10] (skipped 3.11, 3.12) 10-29 reliability, multiple random variables [4.1] 10-30 2-D pdf and CDF [4.2] 11-3 Joint pmf: independent variables: 3x3 example [4.3] 11-5 Joint and conditional pmf, dependent variables: 3x3 example [4.4] 11-6 Dependent variables: f(x,y) = x+y.: joint, marginal, conditional pdf, CDF [4.4] 11-10 Review for MT2 11-12 Conditional pdf, conditional expectation, many dependent variables [4.4 and 4.5] 11-13 MT2 11-17 Function of two variables (sum, product, quotient) 4.6 11-19 Linear transformations (4.6), Expected values of fns of rv's (4.7) 11-20 Jointly Gaussian Variables (4.8) 11-24 Mean Square Estimation (4.9) (skip 4.10) 11-26/27 TXG 12-1 Laws of Large Numbers (5.1, 5.2) 12-3 Central Limit Theorem (IMPORTANT) 12-4 Review