A first undergraduate course in probability and statistics with a focus on discrete spaces. The course is roughly divided in to 4 equal parts with an exam at the end of each part.
Assignment Test: 20%
Quiz 1, Quiz 2: 10% each
Bonus Marks: 5% (For questions based on Bonus Topics).
So weekly there is 4 hrs of classroom time and 6 hrs of homework.
If you are lagging behind, use the online course material [OCW] to catch up. There are also 1-2 buffer classes in each quarter, to help you. If you are already comfortable with the topics, the buffer classes gives you time to explore bonus topics.
Lec 1 : Sample Space | Probability Axioms | Counting
Lec 2 : Conditional Probability | Bayes Rule
Lec 3: Independence | Random Variables
Lec 4: Problem Solving | PMF | Expectation
Office Hrs 1
Lec 5: Expectation | Variance | Conditioning of Random Variables
Lec 6: Multiple Random Variables | Examples: Balls and Bins, Sum of Bernoulli Trials | Independence of RVs
Office Hours 2
Lec 7: Continuos RVs
Lec 8: Multiple Continuos RVs
Lec 9: Continuos Bayes
Lec 10: Markov | Chebyshev
Lec 11: Sum of RVs | Chernoff
Lec 12: Chernoff
Lec 13: Central Limit Theorem
Lec 14: Process | Bernoulli Process
Poisson Process - I
Markov Chains I
Markov Chains II
Markov Chains III
Markov Chains IV
Classical Stat. Inference: (2 lecs) Point Estimates for Mean, Varience | Interval Estimates | Maximum Likelihood | Hypothesis Testing | Linear Regression
Information Theory (2 lecs by Prof. Lalitha)
Bayesian Stat. Inference
Multidimensional Gaussian’s & Kalman Filters
[BT] Introduction to Probability, 2nd Edition by Dimitri P. Bertsekas and John N. Tsitsiklis./
[HPN] Introduction to Probability, Statistics and Random Processes. by Hossien Pishro-Nik. Texbook available online: https://www.probabilitycourse.com/
[WF] An Introduction to Probability Theory and Its Applications, Volume 1 by William Feller.
[SR] Introduction to Probability and Statistics for Engineers and Scientists by Sheldon M. Ross. Available in Library.
[OCW] Probabilistic Systems Analysis and Applied Probability Online Resource. MIT OCW https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/index.htm