Exam P Syllabus
1. General Probability (23%-30%)
The Candidate will understand basic probability concepts, combinatorics, and discrete mathematics.
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.
b) Calculate probabilities using addition and multiplication rules.
c) Define independence and calculate probabilities of independent events.
d) Calculate probabilities of mutually exclusive events.
e) Calculate probabilities using combinatorics, such as combinations and permutations.
f) State Bayes Theorem and the law of total probability and use them to calculate conditional probabilities.
2. Univariate Random Variables (44%-50%)
The Candidate will understand key concepts concerning discrete and continuous univariate random variables (including binomial, negative binomial, geometric, hypergeometric, Poisson, uniform, exponential, gamma, normal, lognormal, and beta) and their applications.
a) Explain and apply the concepts of random variables, probability, probability density functions, and cumulative distribution functions.
b) Calculate conditional probabilities.
c) Explain and calculate expected value and higher moments, mode, median, and percentile.
d) Explain and calculate variance, standard deviation, and coefficient of variation.
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.
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.
g) Determine the sum of independent random variables (Poisson and normal).
3. Multivariate Random Variables (23%-30%)
The Candidate will understand key concepts concerning multivariate discrete random variables, the distribution of order statistics, and linear combinations of independent random variables, along with associated applications.
a) Explain and perform calculations concerning joint probability functions and cumulative distribution functions for discrete random variables only.
b) Determine conditional and marginal probability functions for discrete random variables only.
c) Calculate moments for joint, conditional, and marginal discrete random variables.
d) Calculate variance and standard deviation for conditional and marginal probability distributions for discrete random variables only.
e) Calculate joint moments, such as the covariance and the correlation coefficient for discrete random variables only.
f) Determine the distribution of order statistics from a set of independent random variables.
g) Calculate probabilities for linear combinations of independent normal random variables.
h) Calculate moments for linear combinations of independent random variables.
i) Apply the Central Limit Theorem to calculate probabilities for linear combinations of independent and identically distributed random variables.