Program Overview

Program Overview

The university program in question is a course on Probability and Statistical Inference, denoted as Math 40, scheduled for Winter 2024.

Lecture Plan

The lecture plan is tentative and subject to changes. It covers various topics in probability and statistical inference, including:

• Basic Probability
• Binomial and Poisson distributions
• Continuous random variables, such as Exponential, Gamma, and Beta distributions
• Moment generating functions, Normal and lognormal distributions
• Chebyshev’s inequality, Law of large numbers, and central limit theorem
• Transformations and the delta method

Chapter 2: Continuous Random Variables

This chapter covers:

• Exponential, Gamma, and Beta distributions
• Moment generating functions, Normal and lognormal distributions
• Chebyshev’s inequality, Law of large numbers, and central limit theorem
• Transformations and the delta method

Chapter 3: Multivariate Random Variables

This chapter covers:

• Joint CDF
• Independence
• Conditional density
• Correlation and linear regression
• Bivariate normal distribution
• Joint density upon transformations
• Optimal portfolio allocations
• Multidimensional random vectors

Chapter 4: Four Important Distributions in Statistics

This chapter covers:

• Chi-square distribution
• t- and F-distributions

Chapter 6: Parameter Estimation

This chapter covers:

• Statistics as inverse probability
• Method of moments
• Method of Quantiles
• Statistical properties of an estimator
• Linear estimation
• Estimation of variance and correlation coefficient
• Least squares
• Maximum likelihood

Chapter 7: Hypothesis Testing and Confidence Intervals

This chapter covers:

• Hypothesis testing
• Z, t, and chi-sq tests
• Variance and inverse CDF tests
• Other hypothesis tests
• Confidence interval

Assessment

• Midterm: February 9, 2024
• Final exam (comprehensive): March 9, 2024, 8:00 am