Introduction to Probability and Statistics
Course Topics
- Introduction to Probability
- Basic principles of probability
- Counting techniques and combinatorics
- Conditional probability and independence
- Bayes' theorem and its applications
- 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
- 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
- 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
- Regression Analysis
- Simple linear regression
- Multiple regression and model selection
- Analysis of variance (ANOVA)
- Residual analysis and diagnostics
- 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
Disclaimer
The course syllabus is subject to change at the discretion of the instructor. Any modifications or updates will be communicated in advance.