Part IV — Expectation and Moments

Summarizing distributions by their moments: expectation and variance first, then covariance and correlation for pairs, and the conditional versions — conditional expectation and the laws of total expectation and variance — that power regime and mixture arguments.

Topics

Topic	Focus
Expected Value	Expectation for discrete and continuous random variables, and its properties
Variance	Variance, standard deviation, and standardized random variables
Higher-Order Moments	Skewness, kurtosis, and what higher moments say about tails
Covariance	Covariance and its properties
Correlation	The correlation coefficient and its bounds
Conditional Expectation	Conditional expectation as a random variable
Law of Total Expectation	The law of iterated expectations
Law of Total Variance	Decomposing variance into within- and between-group parts