PJENL Actuario Aptitude Exam study plan

Derive the moment generating function for exponential, gamma, and normal distributions and use it to compute the first three moments of each

Solve 15 integration-by-parts and substitution problems drawn from density and survival-function manipulations

Compute eigenvalues, determinants, and matrix inverses by hand for 3x3 matrices and connect each operation to solving normal equations

Build a one-page error log of every mistake made this week with the corrected reasoning written out

Derive the sampling distributions of the sample mean and sample variance and state the independence result for normal samples

Apply the delta method and central limit theorem to approximate the variance of a transformed estimator

Derive maximum likelihood estimators for Poisson, geometric, and two-parameter gamma samples and verify second-order conditions

Construct uniformly most powerful tests via Neyman-Pearson and compute power functions for simple alternatives

Convert between nominal, effective, and force-of-interest rates and verify each conversion numerically in a spreadsheet

Price annuities-immediate, annuities-due, perpetuities, and m-thly annuities using closed-form accumulation factors

Amortize a level-payment loan and decompose each payment into interest and principal across the full schedule

Compute duration, convexity, and immunization conditions for a two-asset portfolio against a single liability

Derive present values of continuous and discrete life annuities from the survival function and the force of mortality

Compute net single premiums and net annual premiums for term, whole life, and endowment insurance using the equivalence principle

Build a life table from qx values and verify that the resulting lx column reproduces the stated survival probabilities

Calculate expected present values of benefits under a constant-force-of-mortality assumption and compare with the life-table result

Reserve a term and a whole life policy prospectively and retrospectively and show the two reserves agree at every duration

Compute gross premiums with expense loading and decompose the expense-adjusted reserve into its components

Derive the actuarial present value of a benefit contingent on multiple decrement causes and adjust for withdrawal

Set up Thiele's differential equation for a simple policy and solve it for the constant-force case

Derive the adjustment coefficient for exponential and gamma claim-size distributions and state the Lundberg bound

Compute ruin probabilities under the Cramer-Lundberg model for small claim counts using the recursion and compare with the exponential bound

Apply the collective risk model to compute the mean and variance of aggregate claims under frequency-severity independence

Derive the greatest accuracy and Buhlmann credibility factors and compute credibility premiums for a two-year experience period

Solve a Bayesian credibility problem with a conjugate prior and verify the posterior mean equals the credibility premium

Compute net present value, internal rate of return, and payback for capital budgeting scenarios and rank mutually exclusive projects

Derive the CAPM expected return and decompose portfolio variance into systematic and idiosyncratic components

Explain how duration gaps and interest-rate risk transmit through a financial institution's balance sheet

Revisit the credibility and ruin problems missed in week 6 and resolve each without notes

Complete two full-length timed mock exams under exam conditions and log every question by domain and error type

Re-derive from memory the ten formulas most frequently missed across all mocks

Drill the two weakest domains with 20 targeted problems each until accuracy exceeds 80%

Build a final one-page formula sheet restricted to results you can derive rather than recall