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Chapter 1-General Probability Reading 1 Question 4
General Probability
1.a –Define set functions, Venn diagrams, sample space, and events. Define probability as a set function on a collection of events and state the basic axioms of probability.
1.b –Calculate probabilities using addition and multiplication rules.
1.c –Define independence and calculate probabilities of independent events.
1.d –Calculate probabilities of mutually exclusive events.
1.e –Define and calculate conditional probabilities.
1.f –Calculate probabilities using combinatorics, such as combinations and permutations.
1.g –State Bayes Theorem and the law of total probability and use them to calculate conditional probabilities.
Univariate Random Variables
2.a-b –Explain and apply the concepts of random variables, probability and probability density functions, cumulative distribution functions. & Calculate conditional probabilities.
2.c –Explain and calculate expected value, mode, median, percentile, and higher moments.
2.d –Explain and calculate variance, standard deviation, and coefficient of variation.
2.e –Apply the concepts of deductibles, coinsurance, benefit limits, and inflation to convert a given loss amount from a policyholder into the corresponding payment amount for an insurance company.
2.f –Calculate the expected value, variance, and standard deviation of both the loss random variable and the corresponding payment random variable upon the application of policy adjustments.
2.g –Determine the sum of independent random variables (Poisson and normal).
Multivariate Random Variables
3.a –Explain and perform calculations concerning joint probability functions, probability density functions, and cumulative distribution functions.
3.b –Determine conditional and marginal probability functions, probability density functions, and cumulative distribution functions.
3.c –Calculate moments for joint, conditional, and marginal random variables.
3.d –Explain and apply joint moment generating functions.
3.e –Calculate variance, standard deviation for conditional and marginal probability distributions.
3.f –Calculate joint moments, such as the covariance and the correlation coefficient.
3.g –Determine the distribution of a transformation of jointly distributed random variables. & Determine the distribution of order statistics from a set of independent random variables.
3.h –Calculate probabilities and moments for linear combinations of independent random variables.
3.i –State and apply the Central Limit Theorem.
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