Day | Plan |
Sep 4 | - Basic principle of counting (1.2)
- Examples 2a, 2c, 2e
- Permutations (1.3)
- Examples 3b
- Self-test 1a, 1b
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Sep 6 | - Permutations contd. (1.3)
- Self-test 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
- Self-test 1
- Axioms of probability (2.3)
- Examples 3a, 3b
- HW 1 out
|
Sep 18 | - Inclusion-Exclusion 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
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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 (10-11:30 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
- Self-test 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)
- 10-11:30
- 2-3:30
- HWs 10 and 11 due
|
Dec 18 | FINAL EXAM (4-6 in 513 Dennison) |