Probability Theory with Actuarial Applications

ABOUT THE COURSE:This course builds a rigorous foundation in probability with actuarial applications aligned to Exam P. Learners master random variables, distributions, joint/conditional analysis, expectations, and LLN/CLT, and then apply these to insurance contexts such as deductibles, policy limits, aggregate claims, and stop‑loss. Weekly quizzes, worked examples, and a timed mock prepare learners for the certification exam.INTENDED AUDIENCE: Upper‑UG students in Mathematics/Statistics/Economics/CS; actuarial aspirants; early‑career analysts.PREREQUISITES: Single‑variable calculus; basic linear algebra. Week‑0 refresher pack provided.INDUSTRY SUPPORT: Insurance and reinsurance (LIC, GIC Re, Swiss Re), actuarial consulting (EY, Deloitte, PwC), analytics/KPO firms (Genpact, EXL).

Syllabus

Week 1: Probability axioms; sets; counting; Bayes; independence
Week 2:Random variables; CDF/PMF/PDF; expectations; functions of RVs
Week 3:Common distributions: Bernoulli, Binomial, Poisson, Normal, Gamma/Exponential
Week 4:Joint distributions; conditional; covariance/correlation
Week 5:Transformations; Jacobians; order statistics (intro)
Week 6:Law of total expectation/variance; conditioning drills
Week 7:Sums of RVs; convolution; MGFs/CGFs
Week 8:Approximations; inequalities; tail bounds (light)
Week 9:LLN; CLT; Normal approximations; continuity correction
Week 10:Insurance I: loss RVs; deductibles; policy limits; severity/frequency
Week 11:Insurance II: aggregate claims (compound Poisson), stop‑loss, retention
Week 12:Revision; timed mock exam (Exam‑P style)