Probability for Life Science

Lecturer: Prof. Herbert Enderton
College/University: University of California, Los Angeles (UCLA)

1. Events, Sample Space, and Probability Function
   
2. Basic Properties of the Probability Function, Multiplication Principle, Addition Principle, Permutation
   
3. Combinations, Permutation of n Objects Not All Distinct
   
4. Other Properties of the Probabilty Function
   
5. Conditional Probability
   
6. Law of Total Probability, Bayes' Rule, and Independent Events
   
7. Independence of Two or More Events
   
8. Discrete Random Variables, Probability Mass Function, Cumulative Distribution Function, and Expected Value
   
9. Properties of Expected Value, Variance and Standard Deviation of a Random Variable
   
10. Binomial Distribution, Joint Distributions, Independent Random Variables and Other Properties
    
11. Review
    
12. Multinomial Distribution, Geometric Distribution
    
13. Expected Value and Standard Deviation of a Geometric Distribution, Negative Binomial Distribution
    
14. Poisson Distribution
    
15. Expected Value, Variance and Standard Deviation of the Poisson Distribution
    
16. Continuous Random Variable, Probability Density Function
    
17. Mean and Variance of Continuous Random Variable, Exponential Distribution
    
18. Variance and Standard Deviation of an Exponential Distribution, Exponential Distribution with Parameter Lamda as a Function of Another Variable
    
19. Standard Normal Distribution and Its Properties
    
20. Normal Distribution with Mean "Mu" and Standard Deviation "Sigma"
    
21. Central Limit Theorem
    
22. Applications of Central Limit Theorem
    
23. Review
    
24. Confidence Interval (Part I)
    
25. Confidence Interval (Part II)
    
26. Markov's Inequality, Chebyshev's Inequality, Law of Large Numbers
    
27. Determining Sample Size and Confidence Interval
    
28. Review

Probability and Random Variables

Lecturer: Professor M. Chakraborty
College/University: Indian Institute of Technology Kharagpur

1. Introduction to the Theory of Probability
   
2. Axioms of Probability (First Part)
   
3. Axioms of Probability (Second Part)
   
4. Introduction to Random Variables
   
5. Probability Distributions and Density Functions
   
6. Conditional Distribution and Density Functions
   
7. Function of a Random Variable (First Part)
   
8. Function of a Random Variable (Second Part)
   
9. Mean and Variance of a Random Variable
   
10. Moments
    
11. Characteristic Function
    
12. Two Random Variables
    
13. Function of Two Random Variables (First Part)
    
14. Function of Two Random Variables (Second Part)
    
15. Covariance and Correlation
    
16. Vector Space of Random Variables
    
17. Joint Moments
    
18. Joint Characteristic Functions
    
19. Joint Conditional Densities (First Part)
    
20. Joint Conditional Densities (Second Part)
    
21. Sequences of Random Variables (First Part)
    
22. Sequences of Random Variables (Second Part)
    
23. Correlation Matrices and their Properties (First Part)
    
24. Correlation Matrices and their Properties (Second Part)
    
25. Conditional Densities of Random Vectors
    
26. Characteristic Functions and Normality
    
27. Chebychev's Inequality and Estimation
    
28. Central Limit Theorem
    
29. Introduction to Stochastic Process
    
30. Stationary Processes
    
31. Cyclostationary Processes
    
32. System with Random Process at Input
    
33. Ergodic Processes
    
34. Spectral Analysis (First Part)
    
35. Spectral Analysis (Second Part)
    
36. Spectrum Estimation - Non Parametric Methods
    
37. Spectrum Estimation - Parametric Methods
    
38. Autoregressive Modeling and Linear Prediction
    
39. Linear Mean Square Estimation - Wiener (FIR)
    
40. Adaptive Filtering - LMS Algorithm