MTH 2611 - Probability for Actuarial Science I

This course is designed to provide students with a comprehensive understanding of the core mathematical concepts included on the syllabus for the Actuarial Exam in Probability (Exam P, offered by the Society of Actuaries). The topics covered include calculation in general probability, discrete and continuous random variables, multivariate random variables, and risk measurements in actuarial science. The course will place a substantial focus on developing efficient problem-solving skills. 
Prereq: MTH 1110  
Note: None
This course meets the following Raider Core CLO Requirement: None

• 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
• Calculate probabilities using combinatorics, such as combinations and permutations
• Define independence and calculate probabilities of independent events.
• Calculate probabilities of mutually exclusive event
• Calculate probabilities using addition and multiplication rules
• Define and calculate conditional probabilities
• State Bayes Theorem and the law of total probability and use them to calculate conditional probabilities
• Explain and apply the concepts of probability, random variables, probability density functions, and cumulative distribution functions
• Calculate conditional probabilities
• Explain and calculate expected values, including moments, mode, median, and percentile
• Explain and calculate variance, standard deviation, and coefficient of variatio
• Calculate the amount that an insurance company pays to a policyholder for a claim given policy information, including deductibles, coinsurance percentages, and benefit limits, as well as other factors, such as inflation
• Calculate the expected value, variance, and standard deviation of both the loss random variable and the corresponding payment amount random variable
• Determine joint probability functions and joint cumulative distribution functions for discrete random variables
• Determine conditional and marginal probability functions for discrete random variables
• Calculate moments for joint, conditional, and marginal discrete distributions
• Calculate variance and standard deviation for conditional and marginal probability distributions for discrete random variables
• Calculate the covariance and the correlation coefficient for discrete random variables.
• Determine the joint distribution of order statistics for a set of independent random variables
• Calculate probabilities for linear combinations of independent discrete random variables as well as for continuous normal random variables
• Calculate moments for linear combinations of independent random variables
• Apply the Central Limit Theorem to calculate approximations of probabilities for linear combinations of independent and identically distributed random variables

• Calculus

• Basic concepts of probability and discrete mathematics
• Discrete univariate distributions (including binomial, geometric, hypergeometric, negative binomial, Poisson, uniform)
• Continuous univariate distributions (including beta, exponential, gamma, lognormal, normal, and uniform).
• Multivariate distributions
• Central Limit Theorem