Exam P – Probability

3 个单元 · 22 个章节

免费 Exam P – Probability 学习笔记,适合 SOA (Society of Actuaries) 学生。每个章节都覆盖一个重点主题,并附例题与可延伸到 thinka app 的练习提示。

General Probability

  • Set functions, sample spaces, events, and axioms of probability

  • Combinatorial probability: combinations and permutations

  • Independence and probabilities of independent events

  • Mutually exclusive events

  • Addition and multiplication rules

  • Conditional probability

  • Bayes' Theorem and the law of total probability

Univariate Random Variables

  • Random variables, probability density functions, and cumulative distribution functions

  • Conditional probabilities for random variables

  • Expected values: moments, mode, median, and percentiles

  • Variance, standard deviation, and coefficient of variation

  • Insurance payments: deductibles, coinsurance, benefit limits, and inflation

  • Moments of the loss and payment amount random variables

Multivariate Random Variables

  • Joint probability and cumulative distribution functions (discrete)

  • Conditional and marginal probability functions (discrete)

  • Moments for joint, conditional, and marginal distributions

  • Variance and standard deviation for conditional and marginal distributions

  • Covariance and the correlation coefficient

  • Joint distribution of order statistics

  • Probabilities for linear combinations of random variables

  • Moments for linear combinations of random variables

  • The Central Limit Theorem

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