Below is a tentative recap of the main contents of Prob and Stats courses, arranged in a form to identify possible overlaps that could give place to a dedicated topic. Note that the table is still under development, and therefore may be subject to changes (e.g. different aggregation or association with lectures from different courses). This is a good example of where collaborative between students could yield powerful results.

Bit of notation used in the table below: U/M - Unit/Module, L - Lecture, R - Recitation/Solved Problems, PS/HW - Problem Set/Homework.

Topic Probability Statistics
Probability models and axioms U1 L1: Probability models and axioms
(10 Questions)
PS1
(6 Questions)		  
Conditioning and Independence U2 L2: Conditioning and Bayes’ rule
(5 Questions)
U2 L3: Independence
(7 Questions)
PS2
(4 Questions)		  
Counting U3 L4: Counting
(6 Questions)
Problem Set 3
(6 Questions)		  
Discrete random variables U4 L5: PMF and Expectations
(9 Questions)
U4 L6: Variance; Conditioning on an event; Multiple r.v.
(10 Questions)
U4 L7: Conditioning on a random variable; Independence of r.v.
(7 Questions)
Problem Set 4
(6 Questions)		  
Continuous random variables U5 L8: Probability density functions
(7 Questions)
U5 L9: Conditioning on an event; Multiple r.v.’s
(9 Questions)
U5 L10: Conditioning on a random variable; Independence; Bayes’ rule
(11 Questions)
Problem Set 5
(7 Questions)		  
Further topics on random variables U6 L11: Derived distributions
(6 Questions)
U6 L12: Sums of independent r.v.’s; Covariance and correlation
(8 Questions)
U6 L13: Conditional expectation and variance revisited; Sum of a random number of independent r.v.’s
(7 Questions)		 U3 L10: Covariance Matrices
(15 Questions)
Bernoulli and Poisson processes U9 L21: The Bernoulli process
(7 Questions)
U9 L22: The Poisson process
(7 Questions)
U9 L23: More on the Poisson process
(10 Questions)		  
Introduction to statistics U8 L18: Inequalities, convergence, and the Weak Law of Large Numbers
(6 Questions)
U8 L19: The Central Limit Theorem (CLT)
(4 Questions)		 U1 L1: What is statistics
(11 Questions)
U1 L2: Probability Redux
(18 Questions)
U3 L10: Multivariate Statistics
(2 Questions)
Foundation of Inference U8 L20: An introduction to classical statistics
(7 Questions)		 U2 L3: Parametric Statistical Models
(17 Questions)
U2 L4: Parametric Estimation and Confidence Intervals
(17 Questions)
U2 L5: Delta Method and Confidence Intervals
(19 Questions)
U2 L6: Introduction to Hypothesis Testing, and Type 1 and Type 2 Errors
(34 Questions)
U2 L7: Hypothesis Testing (Continued): Levels and P-values
(19 Questions)
U3 L10: Multivariate Statistics
(1 Question)
Methods of Estimation   U3 L8: Distance measures between distributions
(29 Questions)
U3 L9: Introduction to Maximum Likelihood Estimation
(20 Questions)
U3 L10: Consistency of MLE
(5 Questions)
U3 L11: Fisher information, Asymptotic normality of MLE; Method of Moments
(27 Questions)
U3 L12: M-Estimation
(23 Questions)
Hypothesis Testing   U4 L13: Chi Squared Distribution, T-Test
(16 Questions)
U4 L14: Wald’s Test, Likelihood Ratio Test, and Implicit Hypothesis Test
(17 Questions)
U4 L15: Goodness of Fit Test for Discrete Distributions
(19 Questions)
U4 L16: Goodness of Fit Tests Continued: Kolmogorov-Smirnov test, Kolmogorov-Lilliefors test, Quantile-Quantile Plots
(23 Questions)
Bayesian Statistics U7 L14: Introduction to Bayesian inference
(7 Questions)
U7 L16: Least mean squares (LMS) estimation
(6 Questions)		 U5 L17: Introduction to Bayesian Statistics
(23 Questions)
U5 L18: Jeffreys Prior and Bayesian Confidence Interval
(19 Questions)
Linear Regression U7 L15: Linear models with normal noise
(7 Questions)
U7 L17: Linear least mean squares (LLMS) estimation
(7 Questions)		 U6 L19: Linear Regression 1
(21 Questions)
U6 L20: Linear Regression 2
(21 Questions)
U7 L21: Introduction to Generalized Linear Models; Exponential Families
(17 Questions)
U7 L22: GLM: Link Functions and the Canonical Link Function
(8 Questions)
Principal Component Analysis   U8 L23: Principal Component Analysis
Finite-state Markov chains U10 L24: Finite-state Markov chains  
Steady-state behavior of Markov chains U10 L25: Steady-state behavior of Markov chains  
Absorption probabilities and expected time to absorption U10 L26: Absorption probabilities and expected time to absorption  

The general idea for the creation of cheat sheets is to perform the following for each Topic:

  • review the lectures (mainly finger exercises);
  • solve again all PS/HW from scratch;
  • take note of the formulas/concepts in the official answer;
  • identify the link between definitions and the solutions;
  • reduce the links to a minimum set of pairs (definition, solution); and
  • translate these pairs into a cheat sheet for that Topic (work done individually).

Any suggestions as to rearrange or aggregate topics in the comment section below are welcome!