SOA Exam P: Probability (Part 2 of 2) [Actuarial]

Name: SOA Exam P: Probability (Part 2 of 2) [Actuarial]
Rating: 4.7 (6 reviews)

Part 2 of 2 courses covering the content of SOA Exam P/CAS Exam 1

Created byLogenthiran Kanisan

Last updated 4/2023

English

English [Auto],

What you'll learn

Prepare for Society of Actuaries (SOA) Exam P (Probability) [This is part 2 of 2 parts]
Understand key concepts concerning multivariate random variables (including the bivariate normal) and their applications.
Determine the distribution of a transformation of jointly distributed random variables
Determine the distribution of order statistics from a set of independent random variables

Course content

4 sections • 21 lectures • 19h 39m total length

Uniform & Exponential Distributions50:58
This lecture introduces continuous distributions, focusing on the uniform and exponential distributions, deriving density, cdf, mean, and variance, and exploring transformations and memoryless properties.
Normal & Lognormal Distributions1:09:03
Study the normal and lognormal distributions, standard normal concepts, and central limit theorem implications, using phi tables and the moment generating function, with exam P practice.
Law of Averages & Central Limit Theorem59:16
Examine the law of averages and the central limit theorem, using the normal distribution to approximate sample means from random samples, with Chebyshev bounds and continuity corrections.
Gamma & Beta Distributions53:02
Explore gamma and beta distributions, their two-parameter forms and gamma function, including chi-squared as a gamma special case, with connections to exponential, Poisson processes, and exam strategies.
Hazard Rate Function, Pareto Distribution, Weibull Distribution41:46
Explore hazard rate, Pareto and Weibull distributions, and their applications to mortality and machine failure rates, with emphasis on understanding over memorization.
Tutorial - Important Continuous Distributions1:03:01
Explore important continuous distributions: normal, exponential, and uniform, and master density and cdf calculations. Apply central limit theorem concepts to sums and averages in actuarial problems.

Discrete - Joint Distributions, Expectations & Conditional Distributions52:18
Explore discrete joint distributions, marginal and conditional concepts, and how to compute expectations and variances for x and y, with practical examples.
Independence, Covariance, Correlation55:25
Examine independence, covariance, and correlation in joint distributions for actuarial exam P, including testing independence, calculating expectations and covariances, and deriving the correlation coefficient through practical examples.
Continuous - Joint Densities, Expectations48:06
Explores joint densities for two continuous variables, defining the region and marginals, using graphical and integral methods, and computing expectations, variances, and covariances through various examples.
Continuous - Conditional Distributions, Independence, Covariance1:04:03
Explore conditional distributions and independence in continuous joint densities, and compute marginals, covariance, and conditional expectations via region-based double integrals.
Multinomial, Bivariate Normal & Moment Generating Functions34:28
Explore multinomial distributions, bivariate normal properties, and joint moment generating functions. Learn about independence, conditional densities, and practical actuarial examples.
Tutorial - Multivariate Distributions55:33
Explore a hands-on tutorial on continuous joint distributions, marginal densities, and covariance. Tackle problems on device reliability, exponential distributions, and conditional variance using integration.

Transformations & Convolutions59:20
Explore transformations of random variables using the CDF and density techniques, including monotonic transformations, inversion, sums via convolution, and ratios.
Order Statistics1:04:35
Introduce order statistics, rank observations into y1 through yn, derive distributions for the minimum, maximum, and intermediate orders, with iid assumptions and test score style examples.
Covariance, Conditioning Formulas and Mixtures45:16
Explore covariance and conditioning formulas, including double expectation and conditional variance, then apply to mixtures and random sums in the SOA Exam P actuarial context.
Tutorial - Advanced Topics53:14
Explore advanced topics in probability through transformations, the combination of two random variables, order statistics, covariance, mixtures, and conditioning formulas for variance.

Revision Tutorial 11:00:46
Practice revision tutorial 1 on SOA P probability, covering set theory and Venn diagrams, conditional probability and Bayes, transformations, joint distributions, normal and exponential models, order statistics, and fair-game examples.
Revision Tutorial 244:21
Solve revision problems on joint and marginal densities, distributions with deductibles and policy limits, Poisson MGFs, conditional and marginal variance, independence, and birthday problems.
Revision Tutorial 31:31:57
Review moment generating functions, binomial and exponential distributions, two-stage and Bayesian models, and core actuarial applications for SOA exam P.
Revision Tutorial 442:31
Practice-focused revision tutorial solves actuarial probability problems, including normal distributions, independence, joint CDFs, exponential and Poisson models, and Bayesian updates.
Revision Tutorial 51:10:37
Master probability techniques for SOA Exam P with revision tutorial 5, solving problems on marginal and joint densities, variances and covariances, binomial and normal approximations, and practical exam strategies.

Requirements

Knowledge from Part 1 of this course is assumed

Description

Suitable for students looking for an in-depth understanding of concepts tested in SOA Exam P/ CAS Exam 1.
All of the course objectives for SOA Exam P are covered in depth in this course.

Also suitable for actuarial students and practitioners who are looking to brush up their understanding of Probability.

Part 2 covers the following course objectives:

Course Objective 4: Multivariate Random Variables & Distributions

Course Objective 5: Advanced Probability Topics

Summary/Comprehensive: Revision

Exam P is a pre-requisite for Exam FAM and Exam ASTAM/ALTAM and other upper level SOA exams.

Please be sure to refer to the SOA and CAS websites for the most current details regarding the exams.

About the Instructor

I am very passionate about actuarial science and education, and have been actively involved in the actuarial education scene for many years. I have been tutoring students for SOA (Society of Actuaries) exams for 5 years, and have volunteered as the Education Chairperson for the Actuarial Society of Malaysia from 2018 to 2020.

I have also lectured in a number of universities, including Inti International University & Colleges, Universiti Malaya and UCSI University. I am also currently an Industry Advisor at the Asia Pacific University (APU).
I actively volunteer to speak to students about actuarial science, and do mentor students.

Who this course is for:

Students preparing for Society of Actuaries (SOA) Exam P/ Casualty Actuarial Society (CAS) Exam 1

SOA Exam P: Probability (Part 2 of 2) [Actuarial]

What you'll learn

Explore related topics

Course content

Important Continuous Distributions6 lectures • 5hr 37min

Multivariate Probability Distributions6 lectures • 5hr 10min

Advanced Probability Topics4 lectures • 3hr 42min

Revision5 lectures • 5hr 10min

Requirements

Description

Who this course is for: