Instructor:  Arvind Ayyer  
Office:  X15 (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:  F12 at Old Physics Building (OPB)  
Textbook: 
Introduction to probability and statistics for scientists and engineers (6th edition)
by Sheldon M. Ross Elsevier, 2021 ISBN13  9780128243466, 9789351073987 Supplementary Texts: (a) A first course in probability (Eighth Edition) by Sheldon M. Ross Prentice Hall, 2010 ISBN13  9780136033134 (b) Statistics (Fourth Edition) by David Freedman, Robert Pisani and Roger Purves. W. W. Norton and Company, 2007 ISBN13  9780393929720 (c) Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner. 

TAs: 


Tutorials:  Tuesdays 11:00am — 12:00pm in UG block  
Office hours: 

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  1.11.5  Basic statistics  Chap. 1: 1, 2, 4 
2/8    No class 
  
3/8  2.12.3  Descriptive statistics  Chap. 1: 7, 8, 10 Chap. 2: 1, 6(a,c), 7(a) 

5/8  2.42.6  Sample measures  Chap 2: 6(dg), 7(ce), 10, 14, 19  
2  8/8  2.42.6  Chebyshev's inequality  Chap 2: 12, 14, 21, 26(be) 
9/8  Holiday 
  
10/8  3.13.3  Probability axioms  Chap 2: 30(b), 33, 34, 35 Chap 3: 1, 3, 6 

12/8  3.43.5  Sigma algebras  Chap 3: 4, 11, 18, 20  
3  15/8    Holiday 

16/8    Quiz 1 
  
17/8  3.63.7  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 

5  29/8  4.44.5  Expectation and its properties  Chap. 4: 21, 24, 25, 26, 27, 28 
30/8  4.54.6  Moments and variance  Chap. 4: 30(b), 31, 38, 39, 40, 43  
31/8    Holiday 

2/9    Cancelled due to Pravega 

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 

17/9  5.2  Bernoulli, binomial, Poisson and geometric r.v.'s  Chap 5: 2, 6, 8, 10, 11, 12, 17  
8  19/9  5.35.5  Hypergeometric, Uniform and normal r.v.  Chap 5: 18, 21, 22, 24, 29 
20/9    Quiz 3 

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) 

9  26/9  Midsemester exam 

27/9    Revision 
  
28/9  No class (midterm week) 

30/9  No class (midterm week) 

10  3/10  6.16.3  Central limit theorem  Chap 6: 1, 4, 6, 8, 10 
4/10    Midsem discussion 
  
5/10    Holiday 

7/10  6.46.6  Sampling distributions  Chap 6: 18, 19, 22  
11  10/10  7.17.2  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  Onesided interval estimates  Chap 7: 9, 13, 18, 22, 24  
12  17/10  7.37.4  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  8.18.3  Testing of hypotheses, pvalue  Chap 8: 2, 3, 5, 6  
13  24/10  Holiday 

25/10    Discussion 
  
26/10  8.3  Type II error, onesided test  Chap 8: 8, 10, 11, 12  
28/10  8.3  ttest  Chap 8: 17, 21, 24, 26  
14  31/10  8.48.5  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  9.19.3  Least squares estimator  Chap 8: 63, 66(a)
Chap 9: 1, 3 

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  9.59.7  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  11.12  Chisquared test  Chap 11: 1, 2, 5, 6  
17  21/11    Guest lecture by Prof. Shweta Ramdas
Azim Premji University An Introduction to Quantitative Genetics 

18  5/12  25pm  Final Exam 