Chapter 7: Joint Distributions and Independence of Random Variables

Learning Objectives

• Define joint PMFs, PDFs, and CDFs for pairs of random variables and derive marginal distributions from joint distributions
• Define conditional distributions for both the discrete and continuous case, and apply the law of iterated expectation and the law of total variance
• State and apply the definition of independence of random variables, and distinguish independence from uncorrelatedness
• Compute the distribution of functions of two random variables using the Jacobian transformation and the convolution formula
• Derive the distribution of order statistics for i.i.d. random variables
• Compute covariance and the correlation coefficient, and understand their role in measuring linear dependence