Math 40, Winter 2025
Probability and Statistical Inference

The following plan is tentative and subject to changes.

Note: the numbers in the parenthesis represent the corresponding sections of the textbook.

• Basic Probability
• Binomial and Poisson distributions (1.2, 1.3, 1.4, 1.6, 1.7)
• Poisson distributions (1.7), Distribution and density functions (2.1) Links to an external site.

Chapter 2 Continuous random variables

• Exponential, Gamma, and Beta distributions (2.2, 2.3, 2.4, 2.6, 2.14) 
• Exponential, Gamma, and Beta distributions (2.2, 2.3, 2.4, 2.6, 2.14) 
• Moment generating functions, Normal and lognormal distributions 
• Chebyshev’s inequality (2.8), Law of large numbers, and central limit theorem (2.9, 2.10)
• Transformations and the delta method (2.12, 2.13) 

Chapter 3 Multivariate random variables

• Joint CDF (3.1) 
• Independence (3.2) 
• Conditional density (3.3)
• Correlation and linear regression (3.4) 
• Bivariate normal distribution (3.5) 
• Joint density upon transformations (3.6), Optimal portfolio allocations (3.8) 
• Multidimensional random vectors (3.10)
• Review

Midterm 1 pm Feb 6 to 1 pm Feb 7, 2025

Chapter 4 Four important distributions in statistics

• Chi-square distribution (4.2), t- and F-distributions (4.3, 4.4)

Chapter 6 Parameter estimation

• Statistics as inverse probability (6.1), Method of moments (6.2), Method of Quantiles (6.3) 
• Statistical properties of an estimator (6.4) 
• Linear estimation (6.5), Estimation of variance and correlation coefficient (6.6), Least squares (6.7) 
• Maximum likelihood (6.10) 

Chapter 7 Hypothesis testing and confidence intervals

• Hypothesis testing (7.1, 7.2), Z, t, and chi-sq tests (7.3, 7.4)
• Z, t, and chi-sq tests (7.3, 7.4), Variance and inverse CDF tests (7.5, 7.6) 
• Other hypothesis tests (7.7)
• Confidence interval (7.8)

Final exam (comprehensive) - 8:00 am - 11:00 am, March 11, 2025 (Tuesday)