Catholic Tech

Introduction to Probability and Statistics

Course Topics

  1. Introduction to Probability
    • Basic principles of probability
    • Counting techniques and combinatorics
    • Conditional probability and independence
    • Bayes' theorem and its applications
  2. Random Variables and Probability Distributions
    • Discrete and continuous random variables
    • Probability mass function (PMF) and probability density function (PDF)
    • Expected value and variance
    • Common probability distributions: Bernoulli, Binomial, Poisson, Uniform, Normal
  3. Sampling and Estimation
    • Sampling techniques: random sampling, stratified sampling, cluster sampling
    • Point estimation and properties of estimators
    • Confidence intervals for means and proportions
    • Sample size determination
  4. Hypothesis Testing
    • Null and alternative hypotheses
    • Type I and Type II errors
    • One-sample and two-sample tests
    • Chi-square tests for independence and goodness-of-fit
  5. Regression Analysis
    • Simple linear regression
    • Multiple regression and model selection
    • Analysis of variance (ANOVA)
    • Residual analysis and diagnostics
  6. Introduction to Probability and Statistics in Practice
    • Real-world applications of probability and statistics
    • Case studies and examples from various fields
    • Ethical considerations and common pitfalls in data analysis


The course syllabus is subject to change at the discretion of the instructor. Any modifications or updates will be communicated in advance.