Whiteboard-Session-Notes-Probability-and-Statistics

The purpose of this repository is to store/share notes from the whiteboard sessions conducted by Professor Krishnamachari, starting in Fall 2023.

Session 1

• Thursday 12/14/2023
  • Important terminologies and foundational concepts
  • Experiments, Sets, and Events
  • Independance and Exclusivity
  • Review of Combinatorics
• Participants: Dr. Krishnamachari, Elizabeth O, Kae S

Session 2

• Thursday 12/21/2023
  • Conditioal probability
  • Joint probability
  • Marginalization
  • Law of Total Probability
  • Bayes Law
  • Birthday Paradox
  • AI doom
  • Monte Hall Puzzle
  • Belief Network (Bayesian Network)
• Participants: Dr. Krishnamachari, Elizabeth O, Kae S

Session 3

• Friday 02/09/2024
  • Conditinuous random variables
  • Probability density function (PDF)
  • Cumulative distribution function (CDF)
• Participants: Dr. Krishnamachari, Tamoghna S, Elizabeth O, Kae S

Session 4

• Friday 02/16/2024
  • Common Random Variables (r.v.)
    • Descrete
      • Bernoulli
      • Geometric
      • Binomital
    • Continuous
      • Exponential
      • Gaussian and Nomal
      • Uniform
  • Expected Values
  • Riemann–Stieltjes integral

Session 5

• Friday 03/04/2024
  • Problems to do with linearity of expectation
  • Expectation of positive random variables
  • Tail inequalities that relate cdf bounds to expectation and variance
    • Linearity and Expectation
    • Markov's Inequality
    • Chebyshev's Inequality
  • Covariance and Correlation Coefficient
  • Jointly Gaussian

Session 6

• Friday 03/21/2024
  • LLN (Law of Large Number)
  • WLLN (Weak Law of Large Number)
  • SLLN (Strong Law of Large Number)

Session 7

• Friday 03/22/2024
  • MGF (Moment Generating Functions)
  • Characteristic Functions

Session x (Future Session)

• Expectation and variance (Continued)

  • Aside on higher moments: skew and kurtosis)
  • Real life application (Simulating COVID19 Clasasroom Transmission on a University Campus)

• Riemann–Stieltjes integral

• Tail inequalities

  • (v. briefly) Moment generating function and characteristic function of a random variable
  • Chernoff bound

• Specific random variable families

• Simulating a random variable

• Function of a random variable

• Expectations of function

• How to simulate any arbitrary random variable given a uniform random number generator

• Continuous time Markov chains

• Queuing theory

• Continuous time Gaussian process

• Power spectral density and filtering a random process through a linear time invariant filter

• Kalman Filters

• LQG control

• Markov Decision Process

• Multi-armed Bandits

• Basics of detection and estimation theory

• Information theory