Day  Plan 
Sep 4   Basic principle of counting (1.2)
 Examples 2a, 2c, 2e
 Permutations (1.3)
 Examples 3b
 Selftest 1a, 1b

Sep 6   Permutations contd. (1.3)
 Selftest 1c, 1d, 1e, 1f
 Combinations (1.4)
 Basic formula
 Identity (4.1)
 Combinatorial proof of Binomial theorem
 Example 4e

Sep 11   Multinomial Coefficients (1.5)
 Examples 5a, 5b, 5c
 Sample space and events (2.2)
 Examples of experiments and their sample spaces

Sep 13   Sample space and events (2.2)
 Operations (unions, intersections, complements) on events
 de Morgan’s laws
 Selftest 1
 Axioms of probability (2.3)
 Examples 3a, 3b
 HW 1 out

Sep 18   InclusionExclusion principle (2.4)
 Sample spaces having equally likely outcomes (2.5)
 Examples 5a, 5b, 5c, 5d

Sep 20   Conditional Probabilities (3.2)
 Definition (Eq. (2.1))
 Multiplication rule
 Examples 2b, 2d
 HW 1 due
 HW 2 out

Sep 25   Conditional Probabilities (3.2) continued
 Example 2h
 Bayes’ Formula (3.3)
 Examples 3a, parts 1 and 2

Sep 27   Bayes’ Formula (3.3) continued
 Examples 3c, 3k
 Independent events (3.4)
 Examples 4b, 4e
 Independence of multiple events
 HW 2 due
 HW 3 out

Oct 2   Independent Events (3.4) continued
 Examples 4g, 4h
 Conditional probabilities as ordinary probabilities (3.5)
 Random variables (4.1)
 Example 1a

Oct 4   Random variables (4.1) continued
 Example 1c
 Cumulative Distribution Function
 Discrete random variables (4.2)
 probability mass function
 Example 2a
 Expected value (4.3)
 Examples 3a, 3d
 HW 3 due
 HW 4 out

Oct 9   Expected value of a function of a random variable (4.4)
 Example 4a, Proposition 4.1, Corollary 4.1
 Variance (4.5)
 Definition, alternative formula
 Example 5a
 Standard deviation
 Bernoulli random variables (4.6)
 Eq. (6.1)
 Expectation and variance of Bernoulli random variables

Oct 11   Binomial random variables (4.6)
 Eq. (6.2)
 Example 6b
 Expectation and variance (4.6.1)
 Computing distribution function (6.4.2)
 Poisson random variable (4.7)
 Eq. (7.1)
 Example 7b
 HW 4 due
 HW 5 out

Oct 16  NO CLASS (Fall Study Break) 
Oct 18  MIDTERM EXAM (1011:30 in 513 Dennison) 
Oct 23   Poisson random variable (4.7) continued
 Example 7e
 Expected value of sums (4.9)
 Proposition 9.1, Corollary 9.2
 Example 9d, 9e

Oct 25   Introduction to continuous random variables (5.1)
 Expectation and variance (5.2)
 Proposition 2.1
 Corollary 2.1
 The uniform random variable (5.3)
 Example 3a
 Normal random variables (5.4)
 HW 5 due
 HW 6 out

Oct 30   Normal random variable (5.4) continued
 Examples 4a, 4b
 Midterm Student Feedback

Nov 1   Normal approximation to the Binomial (5.4.1)
 Example 4f
 Exponential random variables (5.5)
 Example 5a
 HW 6 due
 HW 7 out

Nov 6   Exponential random variables (5.5) continued
 Examples 5b, 5d
 Memoryless property
 Hazard rate functions (5.5.1)

Nov 8   Hazard rate functions (5.5.1) continued
 Selftest 15a, 15b
 Joint distribution functions (6.1)
 Example 1a
 HW 7 due
 HW 8 out

Nov 13   Joint distribution functions (6.1) continued
 Examples 1c, 1e
 Independent random variables (6.2)

Nov 15   Independent random variables (6.2) continued
 Example 2c
 Proposition 2.1
 Example 2f
 HW 8 due
 HW 9 out

Nov 20   Sums of independent random variables (6.3)
 Formulas (3.1) and (3.2)
 Identically distributed uniform random variables (6.3.1)
 Example 3a
 Normal Random Variables (6.3.3)
 Proposition 3.2
 Example 3c

Nov 22  NO CLASS (Thanksgiving break) 
Nov 27   Poisson and Binomial Random Variables (6.3.4)
 Examples 3e, 3f
 Conditional distributions: Discrete case (6.4)
 Examples 4a, 4b
 HW 9 due
 HW 10 out

Nov 29   Conditional distributions: Continuous case (6.5)
 Examples 5a, 5b
 Geometric Random Variable (4.8.1)

Dec 4 (guest lecture by Mr. Sougata Chaudhuri)   Expectation of sums (7.2)
 Proposition 2.1, Equation (2.2)
 Examples 2a, 2b, 2c, 2f
 Example 2i
 HW 11 out

Dec 6 (guest lecture by Prof. Stilian Stoev)   Expectation of sums (7.2) continued
 Examples 2j, 2n
 Moments of number of events (7.3)
 Example 3a, 3b, 3d

Dec 11   Covariance, variance of sums, correlations (7.4)
 Proposition 4.1, 4.2
 Equation (4.1)
 Example 4b
 Correlation and Equation (4.2)
 Example 4d

Dec 13   Extra office hours (in 454 West Hall)
 1011:30
 23:30
 HWs 10 and 11 due

Dec 18  FINAL EXAM (46 in 513 Dennison) 