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Table of Contents
Chapter 1 Exam-taking and study strategy........................................5
Top Horse, Middle Horse, Weak Horse..........................................................................5
Truths about Exam P.......................................................................................................6
Why good candidates fail................................................................................................8
Recommended study method........................................................................................10
CBT (computer-based testing) and its implications......................................................11
Chapter 2 Doing calculations 100% correct 100% of the time.......13
What calculators to use for Exam P..............................................................................13
Critical calculator tips...................................................................................................17
Comparison of 3 best calculators..................................................................................26
Chapter 3 Set, sample space, probability models.............................27
Chapter 4 Multiplication/addition rule, counting problems...........41
Chapter 5 Probability laws and “whodunit”.....................................48
Chapter 6 Conditional Probability.....................................................60
Chapter 7 Bayes’ theorem and posterior probabilities....................64
Chapter 8 Random variables..............................................................73
Discrete random variable vs. continuous random variable...........................................75
Probability mass function.............................................................................................75
Cumulative probability function (CDF)........................................................................78
PDF and CDF for continuous random variables...........................................................79
Properties of CDF.........................................................................................................80
Mean and variance of a random variable......................................................................82
Mean of a function........................................................................................................84
Chapter 9 Independence......................................................................86
Chapter 10 Percentile, mean, median, mode, moment........................90
Chapter 11 Find ( ) ( ) ( ) ( ) ,,, EXVarXEXYVarXY || ................................94
Chapter 12 Bernoulli distribution.......................................................110
Chapter 13 Binomial distribution........................................................111
Chapter 14 Geometric distribution.....................................................120
Chapter 15 Negative binomial.............................................................128
Chapter 16 Hypergeometric distribution...........................................139
Chapter 17 Uniform distribution........................................................142
Chapter 18 Exponential distribution..................................................145
Chapter 19 Poisson distribution..........................................................168
Chapter 20 Gamma distribution.........................................................172
Chapter 21 Beta distribution...............................................................182
Chapter 22 Weibull distribution..........................................................192
Chapter 23 Pareto distribution............................................................199
Chapter 24 Normal distribution..........................................................206
Chapter 25 Lognormal distribution....................................................211
Chapter 26 Chi-square distribution....................................................220
Chapter 27 Bivariate normal distribution..........................................225
Chapter 28 Joint density and double integration..............................230
Chapter 29 Marginal/conditional density...........................................250
Chapter 30 Transformation: CDF, PDF, and Jacobian Method.....261
Chapter 31 Univariate & joint order statistics..................................278
Chapter 32 Double expectation............................................................296
Chapter 33 Moment generating function...........................................302
14 Key MGF formulas you must memorize...............................................................303
Chapter 34 Joint moment generating function..................................326
Chapter 35 Markov’s inequality, Chebyshev inequality...................333
Chapter 36 Study Note “Risk and Insurance” explained.................346
Deductible, benefit limit.............................................................................................346
Coinsurance.................................................................................................................351
The effect of inflation on loss and claim payment......................................................355
Mixture of distributions..............................................................................................358
Coefficient of variation...............................................................................................362
Normal approximation................................................................................................365
Security loading..........................................................................................................374
Chapter 37 On becoming an actuary…..............................................375
Guo’s Mock Exam....................................................................................377
Solution to Guo’s Mock Exam.................................................................388
Final tips on taking Exam P.....................................................................423
About the author.......................................................................................424
Value of this PDF study manual..............................................................425
User review of Mr. Guo’s P Manual.......................................................425
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