Probability and Statistics

This course introduces a variety of probabilistic and statistical methods for students in scientific disciplines, and develops the skills needed in the simulation of elementary random experiments. No books are required for this course. However, supplementary readings relevant to lecture notes will be suggested from either of the books below.

Murray R. Spiegel, John Schiller, and R. Alu Srinivasan, Probability and Statistics 4th ed. McGraw-Hill.
Elliot A. Tanis and Robert V. Hogg, A Brief Course in Mathematical Statistics. Prentice Hall, NJ.
Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, and Keying Ye, Probability & Statistics for Engineers & Scientists, 9th ed. Prentice Hall, NJ.

Lecture note	Contents
note01.pdf	1. Sample space and events 2. Axioms of probability 3. Combination and binomial coefficients 4. Assignment No.1
note02.pdf	5. Conditional probability and independent events 6. Assignment No.2 & computer project
note03.pdf	7. Discrete Probability Distributions 8. Bernoulli Trials and Binomial Distributions 9. Expectations 10. Expectations with Independent Random Variables 11. Hypergeometric Distribution 12. Assignment No.3 & computer project
note04.pdf	13. Poisson Distributions 14. Assignment No.4 & computer project
note05.pdf	15. Continuous Probability Distributions 16. Expectations and Variances 17. Gamma Distributions 18. Normal Distributions 19. Calculating Probability with Normal Distributions 20. Central Limit Theorem 21. Approximation for Binomial Distribution 22. Assignment No.5
note06.pdf	23. Descriptive Statistics 24. Exploratory Data Analysis 25. Characterizing Distributions 26. Assignment No.6 & computer project
note07.pdf	27. Theoretical Results on Sampling Distributions 28. Confidence Interval for Mean 29. Concept of Statistical Tests 30. One-sided Hypothesis Tests 31. Power of Test 32. Assignment No.7 & computer project 33. Solutions to Assignment No.7
note08.pdf	34. Statistical Inference using R (data set: brick.txt) 35. Inference on Paired Data (data set: heart.csv) 36. Inference on Two Independent Samples (data sets: nerve.txt, line-a.txt, line-b.txt) 37. Simple Linear Regression (data set: time.txt) 38. Assignment No.8
summary.pdf	39. Summary of Important Formulas
normal.pdf	Standard Normal Cumulative Probability Table
Student.pdf	Student t-Distribution Table for Critical Values