Abstract: In this chapter, we first introduce the joint statistical behavior of multiple random variables, and then the focus turns toward the marginal and conditional cdfs, pdfs, and pmfs. In the ...

Epidemiological studies often have missing data, which are commonly handled by multiple imputation (MI). In MI, in addition to those required for the substantive analysis, imputation models often ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

This course builds a rigorous foundation of probability. Topics covered include: basic concepts of probability theory and statistics, counting, axioms of probability, independence, Bayes rule, ...

On a certain track team, the runners all take between 4 and 7 minutes to finish a mile. The probability density function for the length of time it takes a runner to ...