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PnS : Prob & Stats : Probability & Statistics
General Drive Link : MA20205 (Autumn 2025) by ASR
This includes material from Autumn 2025 Semester
Course Instructor for Section 2 (Phy, Instru, CSE) : Dr. Nitin Gupta
MA20205 Autumn 2025 Syllabus - Detailed
Overview (10/10/2025)
Probability (Including relevant set theory)
Random Variables (RV)
Special Distributions
Functions of RV
Joint Distributions
Transformation
Sampling Distribution
Estimation
Hypothesis Testing - Not there for endsems
Solutions (Assignment 1 to 5) by Musaib Bin Bashir (24IM). Awesome guy.
Binomial Approx & Continuity Correction Theory - For Q9 to 11 of Assignment 4
The playlist now has everything from Expectations to end of midsem syllabus (except Hypergeometric). I have to update the first unit (probabilities, and some basic definitions of random variable), but all the hard stuff is here.
From the post Mid-Sem Portions, This includes everything BUT (5.1) Joint Distribution, & (6.2) Transformation of Random Variables
These are mostly enough, but might miss some parts of the syllabus (covers about 90-95%). The material here is enough to apply them, but there are no proofs for any theorems, nor any derivations for formulas/distributions.
Pretty sure this was made by the Course Coordinator, Dr Nitin Gupta. Also available on Moodle for those in Section-2.
This is a topic-wise collection of resources (Specifically which chapters to read for certain topics) : Spreadsheet Repo
Credit to a Keshav Bhatia (Unverified)
Most of the material here is up-to-date, unlike for MA11003. Do double check though, some material and syllabus has changed.
Probability & Statistics NPTEL: NPTEL playlist for PnS (matches syllabus)
CSE 2020 online lectures :
MA2020 CSE2020 Playlist - Spring 2021
Probability & Statistics NPTEL: NPTEL playlist for PnS This matches the syllabus almost exactly.
One of the best courses I have seen, and great professor. Concepts do sometimes go so high level that they don't explain it as much as they could though.
Includes 2. Random Variables (In-depth), 3. Distributions (Surface Level), 4. Functions of RV (In-depth), 5. Joint Distributions (In-depth), 7. Sampling Distribution, 8. Estimation (In-depth), 9. Hypothesis Testing (In-depth)
These are the courses from Khan Academy relevant to MA20205. Be advised that they don't follow our syllabus, and if you want to use them, please cross-check with your syllabus. They are also a bit more surface level, which is honestly better in my opinion.
Random Variables & Some Distributions
Parts of Estimation (Confidence Intervals)
Probability & Statistics by Dr. Gajendra Purohit : I haven't seen the videos, but the topics are vast. Seems like a good option if you want to learn about specific topics (there are videos about specific distributions for example).
Probability & Statistics for Engineers, by Prof. Bruno Clerckx : I haven't seen the videos, but they seem in-depth. Doesn't include topics 7-9 (Sampling, Estimation, Hypothesis Testing).
This is meant to be a guide for you to prepare for the Autumn 2025 PnS Endsems.
This is neither perfect, nor complete. I apologize for any mistakes present, but I am not responsible for any issues caused by them and I would recommend you double check anything important.
Divided into the resources, and guides. A guide tells you how & what resources to use.
This is a collection of best resources (in my opinion). The set of all resources can be found in the "Study Resources" Section below.
My (Pre) MidSem Revision Class - Low Video Quality - 2.5 Hrs
My Post MidSem Lecture Playlist - (No Joint Distr, Random Vectors) - 11 Hrs - Notes made in these lectures.
PnS Notes CSE 2020 - Math Heavy - 132Pgs
NPTEL Playlist - Matches Syllabus - 40 Hrs
Relevant Textbook Chapters (SM Ross or John A Rice) - 9 Chapters
In-Depth Assignment Solns - (Assignment 1-8+ done by Musaib Bin Bashir (GOAT), Assignment 9 by me)
Class Slides (Section-2) - No Derivations/Depth - 10 Slides (~10pgs each)
Prof Nitin Gupta's Notes - Exhaustive, but hard to understand - 150 to 200 Pgs
Follow whatever best fits your situation, preferably in the bulleted order
Revise Pre midsem (either by 1. My Revision, 3. PnS notes, or 7. Class Slides) - 2 Hrs
Learn/Revise Joint Distributions (7. Class Slides or 8. Prof's Notes). Finish assignment 6. - 3 Hrs
Learn Remaining concepts, via 2. My Post MidSem Lectures. Preferably complete, likely read the solutions of Assignment 7, 8, and 9 in parallel. - 12 Hrs
Learn Random Vectors (Lectures 28, 29, 30 of 8. Prof Nitin Gupta's Notes). - 2 Hrs
If you have any doubts in remaining Assignments, read 6. Assignment solns. - 4 Hrs
Practice PYQs if you can. - 2 Hrs
Watch 8.3 Video from 2. My Post Midsem Playlist.
Revise before Exams (7. Class Slides + estimation summary from somewhere else) - 2 Hrs
Revise Pre Midsem (Best is 7. Class Slides, or 1. My Revision Vid, 3. PnS notes) - 1 Hrs
Revise Joint Distributions (7. Class Slides or 8. Prof's Notes). - 1 Hrs
Revise Post Class Test (7. Class Slides; For Estimation (Topic 8) use 2. My Post Midstem Vid/Notes) - 5 Hrs
Practice all assignments (If any doubts, 6. Assignment Solns). Prioritize Assn 6,7,8,9. Then 4,5. - 12 Hrs
Practice PYQs. - 3 Hrs
Watch 8.3 Video from 2. My Post Midsem Playlist.
Revise before Exams (7. Class Slides + estimation summary from somewhere else) - 2 Hrs
Practice all assignments (If any doubts, 6. Assignment Solns). Prioritize 6,7,8,9. Then 4,5. Make sure 1,2,3 is fine too - 15 Hrs
Practice all PYQ's - 3 Hrs
Read the problems in the 8. Prof's Notes - 3 Hrs
Watch 8.3 Video from 2. My Post Midsem Playlist.
Revise before Exams (7. Class Slides + estimation summary from somewhere else) - 2 Hrs
Revise Assignments & PYQs (Basically see the common Q type) - 9 Hrs
Read & practice the problems in the 8. Prof's Notes - 6 Hrs
Watch 8.3 Video from 2. My Post Midsem Playlist.
Peruse the 5. textbook chapters - 6 hrs
Provided you learnt for MidSems.
Revise Pre Midsem & Joint Distribution with 7. Slides - 2 Hrs
Go through Assn 1-6 with 6. Assn Solns. Especially Assn 6 - 2 Hrs
Watch my videos on LC of RV, and Sampling Distributions from 2. My Post Midsem Playlist - 2 Hrs
Go through Assn 7-8 with 6. Assn Solns - 3 Hrs
Go to Assn 9 solns directly (My written version in 6. Assn Solns). Memorize the processes I have mentioned at the start of the doc. - 3 Hrs
Watch 8.3 Video from 2. My Post Midsem Playlist.
Rush through Revisions with 7. Slides - 1 Hr
Best case scenario is you're doing MVP after finishing all assignments, in which case this works well (40+ marks). If you're studying PnS for the first time after class test, this should get you 25-30 marks.
Stack Exchange is the best option for getting an intuition, in my opinion.
The 3. PnS notes are well derived in many places, and is a good reference.
8. Prof's notes derived pretty much everything, but it might not be clear
4. NPTEL lectures are the perfect balance between derivations & explanations IMO.
No idea about 5. Textbook, but from what I saw, it's a good too.
Steve Burton's videos are also excellent.
There is a slight difference between how I taught CI estimation and how sir taught CI estimation. As such, our methods vary a bit (most explicitly in the video, and Assn-9 Solutions), but the final answers should be the same. I explain this mix-up in 8.3.
Make sure you know how to read tables for PDF and CDF values of sampling distributions.
Again, apologies for mistakes, but no responsibility lies with us.
Assignment 8 has some mistakes in the question (Q4 should be 9 times, not 3 times).
An Introduction to Probability and Statistics by V. K. Rohatgi. & A.K. Md. E. Saleh
Mathematical Statistics and Data Analysis by John A. Rice
Probability and Statistical Inference by R.V. Hogg, E.A. Tanis, & D. L. Zimmerman
Introduction to Probability Theory by Paul G. Hoel, Sidney C. Port and Charles J. Stone
Will update later, much harder with the indian govt/court being against Knowledge-sharing
N/A as of 25/08/2025
TBU
Unknown but includes one class test (12th October)
Confirmed, except for the last few sub-units of Topic 5
Till Topic 4 + Parts of Topic 5
That is :
Probability: Classical, relative frequency and axiomatic definitions of probability, addition rule and conditional probability, multiplication rule, total probability, Bayes’ Theorem and independence, problems.
Random Variables: Discrete, continuous and mixed random variables, probability mass, probability density and cumulative distribution functions, mathematical expectation, moments, moment generating function, median and quantiles, Chebyshev’s inequality, problems.
Special Distributions: Discrete uniform, binomial, geometric, negative binomial, hypergeometric, Poisson, continuous uniform, exponential, gamma, Weibull, Pareto, beta, normal, Cauchy distributions, reliability of series and parallel systems, problems. Continuity Corrections, Binomial Approximation.
Function of a Random Variable: Distribution of function of a random variable, problems.
Standard normal tables will also be provided in exam
[Joint Distributions: Joint, marginal and conditional distributions, Independence are useful for solving certain questions (& it's allowed for Section-2), but other methods learnt above can also be used. Hence optional to study.]