MTH 2610 - Probability for Actuarial Science I

• Use combination and permutation to solve related problems
• Apply basic set theory concepts to probability problems
• Use basic probability rules
• Use tree diagrams, Venn diagrams, Venn Box Diagrams to solve probability problems
• Use DeMorgan’s Laws in probability problems
• Identify and solve problems involving conditional probability
• Identify and solve problems involving total probability, Bayes’ Theorem and independence
• Define a discrete random variable and the probability mass function and use them in examples
• Define the cumulative distribution function for discrete random variables and use it to solve related problems
• Define expected value for discrete random variables and use it in related problems
• Solve problems involving conditional expectations of discrete random variables 
• Identify and apply the discrete uniform distribution 
• Identify and apply the binomial distribution
• Identify and apply the geometric distribution
• Identify and apply the negative binomial distribution
• Identify and apply the hypergeometric distribution
• Identify and apply the Poisson distribution
• Define a continuous random variable and the probability density function and use them in examples
• Define the cumulative distribution function for continuous random variables and use it to solve related problems
• Define expected value for continuous random variables and use it in related problems
• Use measures of central tendency, including mean, median, midrange, mode, quartiles and percentiles of data sets, and for continuous random variables
• Use measures of dispersion, including variance and standard deviation, both for discrete and continuous random variables
• Define and apply Moment Generating Function of different discrete distributions
• Use deductible and cap calculations in insurance problems
• Identify and apply the continuous uniform distribution 
• Identify and apply the normal distribution
• Identify and apply the exponential distribution

• Derivatives of functions, Product Rule, Quotient Rule and Chain Rule
• Integrals of functions, substitution, integration by parts
• Geometric series, Taylor polynomials and Taylor series

• Combinatorial probability: Tree diagrams, the multiplication principle, permutation, and combination
• General probability: Set theory review, basic rules of probability, DeMorgan’s Laws, conditional probability, Bayes’ Theorem, independence
• Discrete random variables and their distributions: Probability mass function, cumulative distribution function, expected value (mean)
• Measures of central tendency: Median of a data set, midrange of a data set, mode of a data set, quartiles, and percentiles of a data set
• Measures of dispersion: Variance and standard deviation
• Conditional probabilities: Conditional expectation
• Different types of discrete distributions: Discrete uniform, binomial, geometric, negative binomial, hypergeometric and Poisson
• Continuous random variables and their distributions: Probability density function, cumulative distribution function, expected value, variance, mode, median, percentiles, moment generating function, conditional probabilities, conditional expectation
• Deductibles and caps in insurance
• Different types of continuous random variables: Continuous uniform, exponential, normal