This course on Probability for Actuarial Science aims to prepare students for actuarial probability exams. The learning outcomes include understanding the basics of set theory, probability theory, counting techniques, conditional probability, random variables, different probability distributions, and inequalities. The course teaches skills such as calculating expectations, variances, and moment generating functions, as well as applying various probability distributions. The teaching method involves theoretical explanations, examples, and proofs to enhance understanding. The intended audience for this course is students preparing for actuarial probability exams or anyone interested in gaining a deep understanding of probability theory for actuarial applications.
Overview
Syllabus
Probability: Lesson 1- Basics of Set Theory.
Probability: Lesson 2 - Sample Space, Events and Compound Events.
Probability Lesson 3 - Basics of Probability Theory/ Kolmogorov Axioms.
Inclusion Exclusion Principle, DeMorgan's Law Examples.
Probability Lesson 4 Part 1: Counting Techniques.
Probability Lesson 4 part 2 Counting Techniques.
Probability Lesson 5: Conditional Probability and Multiplication Law of Probability.
Probability Lesson 6: Independent Events.
Lesson 7 Law of Total Probability.
Lesson 8: Bayes rule.
Bayes rule Example.
Lesson 9 :Random Variables - Introduction.
Discrete Random Variables.
Lesson 11 Continuous Random Variables.
Lesson 12 The Expectation of Random Variables.
Lesson 13: Variance of a Random Variable.
Lesson 14: Properties of Expectation and Variance.
Lesson 15: Moment Generating Functions.
Lesson 16 Bernoulli and Binomial Distribution Part 1.
Lesson 16 Binomial Distribution Part 2.
Lesson 17: Geometric Distribution Part 1.
Lesson 17: Geometric Distribution part II.
Lesson 18: Negative Binomial Distribution - Part 1.
Lesson 18: Negative Binomial distribution Part II.
Lesson 19 Hypergeometric Distribution - Introduction.
Poisson Distribution.
Exponential Distribution.
Poisson Process and Gamma Distribution.
Gamma Distribution.
Univariate transformation of a random variable.
Uniform Distribution.
Normal Distribution.
Beta Distribution.
Chi Squared Distribution.
Markov's Inequality - Intuitively and visually explained.
Proof of Markov's Inequality.
Chebyshev’s Inequality.
Introduction to Multivariate Probability Distributions.
Joint Probability Distribution Of Discrete Random Variables.
Joint Probability Mass Function Example.
Probability Density Function Explained.
Taught by
Stat Courses
