Exam P – Probability
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SOA (Society of Actuaries) の学習者向けの無料Exam P – Probability学習ノート。各章のリンクから、要点・例題・練習問題への導線にアクセスできます。
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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