Summarizing Random Variables

This chapter introduces tools for mathematically summarizing distributions.

Expected Value (The Mean)

The weighted average of all possible outcomes.

Variance and Spread

Variance measures the spread of outcomes from the mean. $Var(X) = E[X^2] - (E[X])^2$

Standard Units & Bounds

We can bound probabilities using universal inequalities:

• Markov’s Inequality
• Chebychev’s Inequality

Covariance and Correlation

Covariance measures the linear relationship between two variables. Correlation ($\rho$) standardizes this between -1 and 1.