e-Mathematics > Probability and Statistics
Probability and Statistics
Computer Project
Get started with R
Probability with R
Simulation and Exact Probability
Monty Hall Problem
Probability Histogram
Binomial Distributions
Expectation and Sample Mean
Hypergeometirc Distributions
Capture-Recapture Problem
Poisson Distributions
Spatial Distribution of IED
Gamma Distributions
Normal Distributions
Central Limit Theorem
Continuity Correction
Statistics with R
Summary Statistics
Exploratory Data Analysis
Finding Critical Values
Hypothesis Tests
Data Analysis Demo

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

Lecture note Presentation Contents
note01.pdf slides01.pdf 1. Sample space and events
2. Axioms of probability
3. Combination and binomial coefficients
4. Assignment No.1
note02.pdf slides02.pdf 5. Conditional probability and independent events
6. Assignment No.2 & computer project
note03.pdf slides03.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

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