Instructor: | Arvind Ayyer | ||||||||||||||||||
Office: | X-15 (new wing) | ||||||||||||||||||
Phone number: | (2293) 3215 | ||||||||||||||||||
Email: | (First name) at iisc dot ac dot in | ||||||||||||||||||
Class Timings: | Mondays, Wednesdays and Fridays, 11:00am — 12:00pm | ||||||||||||||||||
Classroom: | F-12 at Old Physics Building (OPB) | ||||||||||||||||||
Textbook: |
Introduction to probability and statistics for scientists and engineers (6th edition)
by Sheldon M. Ross Elsevier, 2021 ISBN-13 - 978-0128243466, 978-9351073987 Supplementary Texts: (a) A first course in probability (Eighth Edition) by Sheldon M. Ross Prentice Hall, 2010 ISBN-13 - 978-0136033134 (b) Statistics (Fourth Edition) by David Freedman, Robert Pisani and Roger Purves. W. W. Norton and Company, 2007 ISBN-13 - 978-0393929720 (c) Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner. |
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TAs: |
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Tutorials: | Tuesdays 11:00am — 12:00pm in UG block | ||||||||||||||||||
Office hours: |
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The date for the midterms and final will be announced later.
Here are the weights for the homework and exams.
All marks will be posted online on Teams.
week | date | sections | material covered | homework and other notes |
1 | 1/8 | 1.1-1.5 | Basic statistics | Chap. 1: 1, 2, 4 |
2/8 | - | No class |
- | |
3/8 | 2.1-2.3 | Descriptive statistics | Chap. 1: 7, 8, 10 Chap. 2: 1, 6(a,c), 7(a) |
|
5/8 | 2.4-2.6 | Sample measures | Chap 2: 6(d-g), 7(c-e), 10, 14, 19 | |
2 | 8/8 | 2.4-2.6 | Chebyshev's inequality | Chap 2: 12, 14, 21, 26(b-e) |
9/8 | Holiday |
- | ||
10/8 | 3.1-3.3 | Probability axioms | Chap 2: 30(b), 33, 34, 35 Chap 3: 1, 3, 6 |
|
12/8 | 3.4-3.5 | Sigma algebras | Chap 3: 4, 11, 18, 20 | |
3 | 15/8 | - | Holiday |
|
16/8 | - | Quiz 1 |
- | |
17/8 | 3.6-3.7 | Conditional probability | Chap 3: 5, 12, 18, 20, 23, 24, 26 | |
19/8 | 3.8, 4.1 | Bayes' formula and independence | Chap. 3: 25, 27, 29, 32, 34, 39, 41, 42 | |
4 | 22/8 | 4.1 | Random variables and cumulative distribution functions | Chap. 4: 1, 2, 3, 4 |
23/8 | - | Discussion |
- | |
24/8 | 4.2 | Discrete random variables | Chap. 3 of AST: 3.1.1, 3.1.2, 3.1.4(a, b) | |
26/8 | 4.2 | Continuous random variables | Chap. 4: 6, 7, 8 Chap. 5 of AST: 5.1.2, 5.1.4, 5.1.8, 5.1.9 |
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5 | 29/8 | 4.4-4.5 | Expectation and its properties | Chap. 4: 21, 24, 25, 26, 27, 28 |
30/8 | 4.5-4.6 | Moments and variance | Chap. 4: 30(b), 31, 38, 39, 40, 43 | |
31/8 | - | Holiday |
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2/9 | - | Cancelled due to Pravega |
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6 | 5/9 | 4.3 | Joint random variables | Chap. 4: 9, 10, 12 (a, b), 13 (a, b) |
6/9 | - | Quiz 2 |
- | |
7/9 | 4.3, 4.5 | Independent random variables | Chap. 4: 12(c), 13(c), 16, 29, 32 | |
9/9 | 4.7 | Covariance | Chap. 4: 38, 45, 50, 52 | |
7 | 12/9 | 4.7 | iid random variables Change of variables formula |
Chap. 4: 11, 51 (refers to Eg 4.5.g, not f), 57 |
13/9 | - | Discussion |
- | |
14/9 | 4.8 | Moment generating functions | Chap. 4: 53, 54 Chap. 6 of AST: 6.3.1, 6.3.2, 6.3.3 |
|
16/9 | 4.9, 5.1 | Limit theorems r.v.'s |
Chap. 4: 55, 56 Chap. 6 of AST: 6.1.6, 6.1.7 |
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17/9 | 5.2 | Bernoulli, binomial, Poisson and geometric r.v.'s | Chap 5: 2, 6, 8, 10, 11, 12, 17 | |
8 | 19/9 | 5.3-5.5 | Hypergeometric, Uniform and normal r.v. | Chap 5: 18, 21, 22, 24, 29 |
20/9 | - | Quiz 3 |
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21/9 | 5.6, 5.8 | Exponential r.v., r.v.'s related to the normal | Chap 5: 23, 27, 29, 37, 43, 44 | |
23/9 | No class (midterm week) |
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9 | 26/9 | Midsemester exam |
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27/9 | - | Revision |
- | |
28/9 | No class (midterm week) |
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30/9 | No class (midterm week) |
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10 | 3/10 | 6.1-6.3 | Central limit theorem | Chap 6: 1, 4, 6, 8, 10 |
4/10 | - | Midsem discussion |
- | |
5/10 | - | Holiday |
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7/10 | 6.4-6.6 | Sampling distributions | Chap 6: 18, 19, 22 | |
11 | 10/10 | 7.1-7.2 | Maximum likelihood estimation | Chap 6: 23, 24, 27 Chap 7: 1, 2 |
11/10 | - | Quiz 4 |
- | |
12/10 | 7.3 | Interval estimates | Chap 7: 8, 10, 11 | |
14/10 | 7.3 | One-sided interval estimates | Chap 7: 9, 13, 18, 22, 24 | |
12 | 17/10 | 7.3-7.4 | Estimating variance, difference of normals | Chap 7: 35, 36, 41, 42, 43 |
18/10 | - | Quiz 5 |
- | |
19/10 | 7.5, 7.7 | Mean of Bernoullis, estimator bias | Chap 7: 48, 49, 50, 53, 56 | |
21/10 | 8.1-8.3 | Testing of hypotheses, p-value | Chap 8: 2, 3, 5, 6 | |
13 | 24/10 | Holiday |
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25/10 | - | Discussion |
- | |
26/10 | 8.3 | Type II error, one-sided test | Chap 8: 8, 10, 11, 12 | |
28/10 | 8.3 | t-test | Chap 8: 17, 21, 24, 26 | |
14 | 31/10 | 8.4-8.5 | Means of two normals, variance of normals | Chap 8: 27, 29, 31, 35, 38 |
1/11 | - | Holiday |
- | |
2/11 | 8.6 | Bernoulli pops, equality of Bernoullis | Chap 8: 47, 58, 59 | |
4/11 | 9.1-9.3 | Least squares estimator | Chap 8: 63, 66(a)
Chap 9: 1, 3 |
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15 | 7/11 | 9.3 | Distribution of estimators | Chap 9: 6, 8, 9(a) |
8/11 | - | Holiday |
- | |
9/11 | 9.4 | Statistical inferences | Chap 9: 11, 14, 15, 16, 17(d,e) | |
11/11 | 9.5-9.7 | Coefficient of determination | Chap 9: 24, 25, 31, 33 | |
16 | 14/11 | 9.10 | Multiple linear regression | Chap 9: 43, 45 |
15/11 | - | Quiz 6 |
- | |
16/11 | 9.10 | Multiple linear regression | Chap 9: 46, 49, 54(a,c) | |
18/11 | 11.1-2 | Chi-squared test | Chap 11: 1, 2, 5, 6 | |
17 | 21/11 | - | Guest lecture by Prof. Shweta Ramdas
Azim Premji University An Introduction to Quantitative Genetics |
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18 | 5/12 | 2-5pm | Final Exam |