FAD1015 - Mathematics III

PASUM Foundation course covering Statistics and Probability Theory with applications in R programming and matrix algebra.

Course Overview

This course introduces students to fundamental concepts in probability theory, statistical distributions, hypothesis testing, and matrix operations.

Topics Covered

1. Probability Fundamentals (Weeks 1-3)

  • Counting Rules & Permutations
  • Mutually Exclusive Events & Conditional Probability
  • Independent Events & Bayes' Theorem

2. Random Variables (Weeks 4-6)

  • Discrete Random Variables (PDF & CDF)
  • Mean & Variance (Discrete & Continuous)
  • Continuous Random Variables

3. Probability Distributions

  • Binomial Distribution — discrete, fixed trials
  • Poisson Distribution — discrete, rate-based
  • Normal Distribution — continuous, bell curve
  • Uniform Distribution — continuous, equal probability
  • Exponential Distribution — continuous, memoryless

4. Statistical Inference

  • Sampling Distribution of the Mean
  • Estimation of Population Mean
  • Hypothesis Testing About the Mean
  • Hypothesis Testing in R

5. R Programming

  • Input Data & Descriptive Statistics in R
  • Sampling Methods
  • Statistical Computations

6. Linear Algebra

  • Matrices — Types & Operations
  • Matrices — Inverse & Systems of Equations

Lecture Sources

  1. FAD1015 Week 1 — Counting Rules & Permutation
  2. FAD1015 Week 2 — Mutually Exclusive & Conditional Probability
  3. FAD1015 Week 3 — Independent Events & Bayes' Theorem
  4. FAD1015 Week 4 — Discrete Random Variables (PDF & CDF)
  5. FAD1015 Week 5 — Mean & Variance (Discrete & Continuous)
  6. FAD1015 Week 6 — Continuous Random Variables
  7. FAD1015 L13 — Binomial Distribution
  8. FAD1015 L14 — Poisson Distribution
  9. FAD1015 L15-L16 — Normal Distribution & Approximation
  10. FAD1015 L17-L18 — Uniform & Exponential Distributions + R Intro
  11. FAD1015 L19 — Input Data & Descriptive Statistics in R
  12. FAD1015 L20 — Sampling Distribution of the Mean
  13. FAD1015 L21-L22 — Estimation of Population Mean
  14. FAD1015 L23-L24 — Hypothesis Testing About the Mean
  15. FAD1015 L25-L26 — Hypothesis Testing in R
  16. FAD1015 L27-L28 — Matrices (Types & Operations)
  17. FAD1015 L29-L30 — Matrices (Inverse & Systems of Equations)

Tutorial Sources

  1. FAD1015 Tutorial 1-6 — Counting & Probability Fundamentals
  2. FAD1015 Tutorial 7 — Normal Distribution
  3. FAD1015 Tutorial 8 — Uniform & Exponential Distributions
  4. FAD1015 Tutorial 9 — Sampling Methods
  5. FAD1015 Tutorial 10 — Estimation of Population Mean
  6. FAD1015 Tutorial 11 — Hypothesis Testing About the Mean
  7. FAD1015 Tutorial 12 — Hypothesis Testing in R

Past Year Finals

Related Courses

Institution

Universiti Malaya — Centre for Foundation Studies in Science (PASUM)