Guo′s Manuals SOA exam C-ASA北美精算师考试.pdf

Deeper Understanding, Faster Calculation --Exam C Insights Shortcuts 6th Edition by Yufeng Guo Fall 2009 The Missing Manual This electronic book is intended for individual buyer use for the sole purpose of preparing for Exam C. This book can NOT be resold to others or shared with others. No part of this publication may be reproduced for resale or multiple copy distribution without the express written permission of the author. © 2009, 2010 By Yufeng Guo Guo Fall 2009 C, Page 1 / 284 Table of Contents Introduction 4 Chapter 1 Doing calculations 100% correct 100% of the time.. 5 6 strategies for improving calculation accuracy 5 6 powerful calculator shortcuts 6 #1 Solve ax2 + bx + c = 0 . 6 #2 Keep track of your calculation 10 #3 Calculate mean and variance of a discrete random variable 21 #4 Calculate the sample variance 29 #5 Find the conditional mean and conditional variance 30 #6 Do the least squares regression 36 #7 Do linear interpolation 46 Chapter 2 Maximum likelihood estimator 52 Basic idea 52 General procedure to calculate the maximum likelihood estimator 53 Fisher Information 58 The Cramer-Rao theorem 62 Delta method 66 Chapter 3 Kernel smoothing 75 Essence of kernel smoothing 75 Uniform kernel 77 Triangular kernel 82 Gamma kernel 90 Chapter 4 Bootstrap 95 Essence of bootstrapping 95 Recommended supplemental reading 96 Chapter 5 Bühlmann credibility model 102 Trouble with black-box formulas 102 Rating challenges facing insurers 1