Joint, Marginal, and Conditional Distributions (SOA Exam P – Multivariate Random Variables)
Автор: AnalystPrep
Загружено: 2023-05-02
Просмотров: 7378
Описание:
Master joint, marginal, and conditional distributions for SOA Exam P. In this lesson we build PMFs/PDFs and CDFs for multivariate random variables, work through an insurance risk–loss example, use the law of total probability for marginals, and compute conditional probabilities/distributions correctly (joint ÷ marginal). Perfect refresher before attempting practice problems.
AnalystPrep Actuarial Exams Study Packages (video lessons, study notes, question bank, and quizzes) can be found at https://analystprep.com/shop/actuaria...
After completing this video you should be able to:
Explain and perform calculations concerning joint probability functions and cumulative distribution functions for discrete random variables only.
Joint Probability (Density) Function
𝑓_(𝑟,𝑥)=𝑓_(𝑅,𝑋) (𝑟,𝑥)=Pr(𝑅=𝑟∩𝑋=𝑥)
(Joint) Cumulative Distribution Function
𝐹_(𝑅,𝑋) (𝑟,𝑥)=Pr(𝑅≤𝑟∩𝑋≤𝑥)
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