The
Rational Argumentator
Free Tools for Rational Education
The Actuary's Free Study Guide for
Exam 3L
First Edition Published in August-October 2008
Second Edition Published in July 2014
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Click here to download a free PDF copy of the Second Edition of this study guide.
Table of Contents
|
Section |
Page |
|
Section 1:
Life-Table Probability Functions: Practice Problems
and Solutions – Part 1 |
4 |
|
Section 2:
Life-Table Probability Functions: Practice Problems and Solutions –
Part 2 |
6 |
|
Section 3:
Curate-Future-Lifetime |
8 |
|
Section 4:
Force of Mortality |
10 |
|
Section 5:
Identities Involving Life Table Functions and Force of Mortality |
12 |
|
Section 6:
Life-Table Probability Functions: Practice Problems and Solutions –
Part 3 |
14 |
|
Section 7:
Life-Table Probability Functions: Practice Problems and Solutions –
Part 4 |
16 |
|
Section 8:
Deterministic Survivorship Groups |
19 |
|
Section 9:
Computing Expected Values for Continuous Random Variables |
21 |
|
Section 10:
Complete-Expectation-of-Life |
23 |
|
Section 11:
Median Future Lifetime |
25 |
|
Section 12:
Computing Expected Values for Discrete Random Variables |
28 |
|
Section 13:
Life-Table Probability Functions: Practice Problems and Solutions –
Part 5 |
31 |
|
Section 14:
Life-Table Probability Functions: Practice Problems and Solutions –
Part 6 |
33 |
|
Section 15:
The Uniform-Distribution-of-Deaths Assumption for Fractional Ages |
36 |
|
Section 16:
The Uniform-Distribution-of-Deaths Assumption for Fractional Ages:
Practice Problems and Solutions – Part 2 |
38 |
|
Section 17:
Exam-Style Questions on Life-Table Functions – Part 1 |
40 |
|
Section 18:
Exam-Style Questions on Life-Table Functions – Part 2 |
44 |
|
Section 19:
Temporary Complete Life Expectancy |
47 |
|
Section 20:
Recursion Formulas |
49 |
|
Section 21:
Term Life Insurance |
51 |
| Section 22:
Moments of the Present Value of a Term Life Insurance Policy |
54 |
|
Section 23:
Whole Life Insurance |
57 |
|
Section 24:
Makeham's Law of Mortality |
60 |
|
Section 25:
Weibull's Law of Mortality |
63 |
|
Section 26:
Probability Density Functions and Cumulative Distribution Functions of
Present-Value Random Variables |
65 |
|
Section 27:
Pure Endowments |
68 |
|
Section 28:
Endowment Insurance |
71 |
|
Section 29:
Deferred Life Insurance |
76 |
|
Section 30:
Annually Increasing Whole Life Insurance |
80 |
|
Section 31:
Continuously Increasing Whole Life Insurance |
84 |
|
Section 32:
Annually Decreasing Term Life Insurance |
88 |
|
Section 33:
Insurances Payable at the End of the Year of Death |
92 |
|
Section 34:
Whole Life Insurance Payable at the End of the Year of Death |
95 |
|
Section 35:
Endowment Insurance Payable at the End of the Year of Death |
98 |
|
Section 36:
Exam-Style Questions on Life Insurance Policies |
101 |
|
Section 37:
Continuous Whole and Temporary Life Annuities |
105 |
|
Section 38:
Variances and Relationships Among Present Values of Continuous Whole
and Temporary Life Annuities |
108 |
|
Section 39:
Continuous Deferred Life Annuities and Certain and Life Annuities |
111 |
|
Section 40: Actuarial Accumulated Values and Derivatives of
Actuarial Present Values of Continuous Life Annuities |
115 |
|
Section 41: Discrete Whole Life Annuities |
117 |
|
Section 42:
Discrete Temporary Life Annuities |
119 |
|
Section 43:
Discrete Deferred Life Annuities and Certain and Life Annuities |
121 |
|
Section 44:
The Equivalence Principle and Fully Continuous Benefit Premiums for
Whole, Term, and Endowment Life Insurance Policies |
124 |
|
Section 45:
Fully Continuous Benefit Premiums for Pure Endowments and Exam-Style
Questions on Life Insurance and Life Annuities |
128 |
|
Section 46:
Exam Style Questions on Life Table Functions for Independent Lives and
Multiple Causes of Decrement |
133 |
|
Section 47: The Pareto and Weibull Probability Distributions |
138 |
|
Section 48:
The Negative Binomial Distribution and Some Associated Mixture
Distributions |
140 |
|
Section 49:
The Lognormal Probability Distribution, Markov Chains, and Assorted
Exam-Style Questions |
142 |
|
Section 50:
Probability Generating Functions, Poisson Processes, and Assorted
Exam-Style Questions |
145 |
|
Section 51:
Binomial, Pareto, and Compound Probability Distributions |
149 |
|
Section 52:
Fully Discrete Benefit Premiums, Infinite Divisibility Property for
Some Probability Distributions, and Assorted Exam-Style Questions |
152 |
|
Section 53:
Order Statistics, Likelihood Functions, and Maximum Likelihood Estimates |
157 |
|
Section 54:
Exam-Style Questions on the Method of Moments, Significance Levels, and
the Neyman-Pearson Lemma |
161 |
|
Section 55:
Chi-Square Goodness-of-Fit Test |
167 |
|
Section 56:
Hypothesis Testing: Type I and Type II Errors, P-Values, and the
Student-t Distribution |
172 |
|
Section 57:
Least-Squares Regression and Assorted Exam-Style Questions |
176 |
|
Section 58:
Fully Discrete Benefit Reserves |
179 |
|
Section 59:
The Central Limit Theorem and the Continuity Correction for Normal
Approximations |
183 |
|
Section 60:
Characteristics of Estimators, Mean Square Error, and Assorted Exam
Style Questions |
186 |
|
Section 61:
Residuals in Linear Regression and Assorted Exam-Style Questions |
189 |
|
Section 62:
Assorted Exam-Style Questions on Compound Poisson Processes, Normal
Approximations, Force of Mortality, and Multiple Forces of Decrement |
192 |
|
Section 63:
Exam-Style Questions on Markov Chains and Percentile Calculations |
196 |
|
Section 64:
Poisson Processes and the Gamma Distribution |
201 |
|
Section 65:
The F Distribution and Hypothesis Testing of Variances |
204 |
|
Section 66:
Joint-Life Status and Last-Survivor Status |
208 |
|
Section 67:
Assorted Exam-Style Review Questions for Actuarial Exam 3L |
211 |
|
Section 68:
Challenging Exam-Style Review Questions for Actuarial Exam 3L |
214 |
|
Section 69:
Exam-Style Questions for Actuarial Exam 3L – Part 3 |
218 |
|
Section 70:
Pooled Sample Variances and Covariances for Multiple-Life Statuses |
222 |
|
Section 71:
The Coefficient of Determination in Linear Regression, Fully Continuous
Benefit Reserves Under DeMoivre's Law, and Assorted Exam-Style Questions |
226 |
|
Section 72:
Chi-Square Test for the Variance and Assorted Exam-Style Questions |
230 |
|
Section 73:
Exam-Style Questions for Actuarial Exam 3L – Part 4 |
234 |
|
Section 74:
Exam-Style Questions for Actuarial Exam 3L – Part 5 |
238 |
|
Section 75:
Exam-Style Questions for Actuarial Exam 3L – Part 6 |
240 |
|
Section 76:
Exam-Style Questions for Actuarial Exam 3L – Part 7 |
243 |
|
Section 77:
Exam-Style Questions for Actuarial Exam 3L – Part 8 |
246 |
|
About Mr.
Stolyarov |
248 |
Gennady Stolyarov II (G. Stolyarov II) is an actuary, science-fiction novelist, independent philosophical essayist, poet, amateur mathematician, composer, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress.
In December 2013, Mr. Stolyarov published Death is Wrong, an ambitious children’s book on life extension illustrated by his wife Wendy. Death is Wrong can be found on Amazon in paperback and Kindle formats.
Mr. Stolyarov has contributed articles to the Institute for Ethics and Emerging Technologies (IEET), The Wave Chronicle, Le Quebecois Libre, Brighter Brains Institute, Immortal Life, Enter Stage Right, Rebirth of Reason, The Liberal Institute, and the Ludwig von Mises Institute. Mr. Stolyarov also published his articles on Associated Content (subsequently the Yahoo! Contributor Network) from 2007 until its closure in 2014, in an effort to assist the spread of rational ideas. He held the highest Clout Level (10) possible on the Yahoo! Contributor Network and was one of its Page View Millionaires, with over 3.1 million views.
Mr. Stolyarov holds the professional insurance designations of Associate of the Society of Actuaries (ASA), Associate of the Casualty Actuarial Society (ACAS), Member of the American Academy of Actuaries (MAAA), Chartered Property Casualty Underwriter (CPCU), Associate in Reinsurance (ARe), Associate in Regulation and Compliance (ARC), Associate in Personal Insurance (API), Associate in Insurance Services (AIS), Accredited Insurance Examiner (AIE), and Associate in Insurance Accounting and Finance (AIAF).
Mr. Stolyarov has written a science fiction novel, Eden against the Colossus, a philosophical treatise, A Rational Cosmology, a play, Implied Consent, and a free self-help treatise, The Best Self-Help is Free. You can watch his YouTube Videos. Mr. Stolyarov can be contacted at gennadystolyarovii@gmail.com.
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Learn about Mr. Stolyarov's novel, Eden against the Colossus, here.Read Mr. Stolyarov's comprehensive treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, here.