UM 201: Probability and Statistics

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.
TAs:
  • Ajay Nair (ajaynair at iisc dot ac dot in)
  • Hiranya Dey (hiranyadey at iisc dot ac dot in)
  • Anita Arora (anitaarora at iisc dot ac dot in)
  • Dipnit Biswas (dipnitbiswas at iisc dot ac dot in)
  • Geethika Sebastian (geethikas at iisc dot ac dot in)
Tutorials: Tuesdays 11:00am — 12:00pm in UG block
Office hours:
Instructor/TA Office (in Maths dept) Office Hours (5-6pm)
Arvind Ayyer X-15 Mondays
Ajay Nair X-21 Tuesdays
Anita Arora L-24 Wednesdays
Hiranya Dey N-22 Thursdays
Dipnit Biswas X-22 Fridays

Course Description

Basic notions of probability, conditional probability and independence, Bayes'
theorem, random variables and distributions, expectation and variance,
conditional expectation, moment generating functions, limit theorems. Samples
and sampling distributions, estimations of parameters, testing of hypotheses,
regression, correlation and analysis of variance.

Exams

All exams will be closed book, closed notes, and
no calculators or electronic devices are allowed (no cell/smart phones).
No communication among the students will be tolerated.
There will be no make up exams.

The date for the midterms and final will be announced later.

Grading

Here are the weights for the homework and exams.
All marks will be posted online on Teams.

Tentative Class Plan

Tutorials are marked in green.

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
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
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 5.3-5.5 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 6.1-6.3 Central limit theorem Chap 6: 1, 4, 6, 8, 10
4/10 -

Midsem discussion

 -
5/10 -

Holiday
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
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
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
18 5/12 2-5pm

Final Exam