
Explore probability for actuaries across five modules, covering joint, marginal, and conditional distributions; transformations; sums of independent variables; order statistics; central limit theorem; deductibles, policy limits, and coinsurance.
Explore joint distributions for two random variables, both discrete and continuous, by computing joint PMFs and PDFs, evaluating probabilities, and deriving the joint CDF.
Explore conditional distributions and learn to compute X given Y and Y given X using joint and marginal pdfs, with discrete and continuous cases and actuarial examples.
Explore variance, covariance, and correlation, including conditional variance and moments from joint distributions. Apply linear-combination formulas, assess independence, and interpret the correlation coefficient through practical examples.
Learn the joint moment generating function for two random variables, derive moments and covariance via derivatives, and use independence to factor the joint MGF into marginals.
Apply the law of total expectation, or tower rule, through E[E[X|Y]] = E[X] and Var(X) = E[Var(X|Y)] + Var(E[X|Y]), with Poisson and binomial examples.
Explore transformations of a single continuous random variable, deriving the transformed pdf via inverse and cdf methods with examples like Y = T^3 and Y = 3 ln X.
Explore transformations of joint variables and Jacobian method to derive pdf of (U,V) from (X,Y), with examples U = X/Y, V = Y and U = X+Y, V = X−Y.
Apply the convolution method to obtain the distribution of the sum of two random variables. Explore discrete PMFs and continuous PDFs, with independent cases and gamma connections.
Examine the distribution of the sum of independent random variables, compute the variance for mutually independent sums, and apply moment generating and probability generating functions for binomial and gamma cases.
Derive the CDFs for the max and min of independent random variables and extend to multiple variables, then apply to examples like bids, IPO estimates, and exponential times.
Explore order statistics, derive and apply their PDFs and CDFs for minimum and maximum, and analyze joint distributions with exponential examples.
Explains the bivariate normal distribution, including the joint distribution, conditional expectation and variance for X and Y, independence when rho=0, and computing conditional probabilities with examples.
Learn how insurance pools premiums to transfer risk from policyholders to insurers and how actuaries set premiums and reserves. Understand diversification's role in reducing risk as the pool grows.
Explore deductibles, including ordinary, franchise, and disappearing types, and calculate their impact on expected claim costs using vet bills, animal health claims, and exponential models.
Introduces security loading and the gross premium formula P = (1+theta) E[Y], then applies it to a uniform loss example and a deductible with a policy limit.
Are you studying for your first actuarial exam? Do you want to one day work as an Actuary, which is consistently ranked as a top 10 career?
Well then, you’ve come to the right place!
This is where you start. And it is the perfect time to start. Actuaries are in high demand globally. Actuaries can earn a great living and enjoy great job satisfaction.
To become a fully qualified actuary, you have to pass a series of professional exams. Most students start by taking a related university degree. This course along with Part 1 and Part 2 to the course, will provide you with the skills required to pass the first actuarial exam.
Whether you are writing with the Society of Actuaries (SOA) or Casualty Actuarial Society (CAS), this course is for you. The material for SOA Exam P or CAS Exam 1 is covered in this course and Part 1 and 2 to this course.
Part 3 will cover the following areas of the exam:
Joint Distributions, Marginal Distributions and Conditional Distributions
Joint Expected Values
Conditional Expected Values and Conditional Variance
Covariance and Correlation
Independence
Joint Moment Generating Functions
Law of Total Expectation
Transformations - Single Random Variables (Discrete and Continuous)
Transformations - Joint Random Variables
Sum of Independent Random Variables (Convolution Method and Common Distributions)
Sum of Independent Random Variables (Moment Generating Functions and Probability Generating Functions)
Distribution of the Minimum or Maximum of Independent Random Variables
Order Statistics
Central Limit Theorem and Bivariate Normal Distribution
Insurance Related Concepts (Deductibles, Policy Limits, Coinsurance / Proportional Insurance, Security Loadings)
Practice makes perfect with actuarial exams. As such, we have included many practice problems for you to hone your skills. The SOA also provides sample questions and we highly recommend that you practice your skills on these questions as well.
Teaching is my passion!
I have been teaching actuaries around the world since 2014 and have helped 100s of actuaries pass actuarial exams. I have also taught at the University level, teaching courses on probability and mathematical statistics. My teaching style focuses on explaining concepts and then illustrating those concepts with lots of examples. I find that this allows the students to understand the basics and then directly tie the theory to practical applications with practice problems. This sets the students up for success with the actuarial exams that they intend to write.
Why take this course?
This course (along with Part 1 and Part 2) is designed to cover the SOA Exam P/CAS Exam 1 syllabus in entirety. This course is specifically tailored to the actuarial exam. There are a lot of other courses that teach probability and statistics, however, they are more general in nature, whereas this course focuses exclusively on getting you to a passing grade come exam day. My course also offers you lifetime access to the material and was priced at a price point that would be affordable to students around the world.
What you get with this course?
You get access to over 17 hours of video lectures that cover the entire syllabus, split between Part 1, Part 2 and Part 3. You also get access to an electronic manual for the course and over 100 practice questions to hone your skills and prepare you for the actual exam day.