This course provides a comprehensive introduction to probability and statistics, covering essential concepts and techniques. Key topics include:
- Algebra of sets
- Introduction to probability
- Random variables and probability distributions
- Moments and moment generating functions
- Markov and Chebyshev inequalities
- Special discrete and continuous distributions
- Functions of a random variable
- Joint distributions and bivariate normal distribution
- Transformation of random vectors
- Central limit theorem and sampling distributions
- Point estimation techniques including unbiasedness and consistency
- Methods of moments and maximum likelihood estimation
- Confidence intervals for one-sample and two-sample problems
- Testing of hypotheses, including Neyman-Pearson lemma
- Tests for one-sample and two-sample problems
Join us to gain a solid foundation in probability and statistics, essential for various fields including data science, finance, and research.