The "2024 FRM Exam Part I – Quantitative Analysis PDF" by GARP (Global Association of Risk Professionals) is a vital resource for candidates preparing for the FRM Exam Part I. This official guide focuses on the essential quantitative techniques required for analyzing and managing risk in financia...
Chapter 1 Fundamentals Chapter 2 Random Variables 11
of Probability 1
2.1 Definition of a Random Variable 12
1.1 Sample Space, Event Space, 2.2 Discrete Random Variables 13
and Events 2
2.3 Expectations 14
Probability 2
Properties of the Expectation Operator 14
Fundamental Principles of Probability 4
Conditional Probability 4 2.4 Moments 14
Example: SIFI Failures 5 The Four Named Moments 16
Moments and Linear Transformations 17
1.2 Independence 5
Conditional Independence 6 2.5 Continuous Random Variables 18
1.3 Bayes' Rule 7 2.6 Quantiles and Modes 20
1.4 Summary 7 2.7 Summary 22
Questions 8 Questions 23
Short Concept Questions 8 Short Concept Questions 23
Practice Questions 8 Practice Questions 23
Answers 9 Answers 24
Short Concept Questions 9 Short Concept Questions 24
Solved Problems 9 Solved Problems 25
iii
, 4.2 Expectations and Moments 51
Chapter 3 Common Univariate Expectations 51
Random Variables 27 Moments 52
The Variance of Sums of Random
Variables 53
3.1 Discrete Random Variables 28 Covariance, Correlation,
Bernoulli 28 and Independence 54
Binomial 29
4.3 Conditional Expectations 55
Poisson 30
Conditional Independence 55
3.2 Continuous Random Variables 31
4.4 Continuous Random Variables 56
Uniform 31
Marginal and Conditional Distributions 57
Normal 32
Approximating Discrete Random 4.5 Independent, Identically
Variables 34 Distributed Random Variables 57
Log-Normal 34 4.6 Summary 58
2
x 36
Student's t 37 Questions 59
F 38 Short Concept Questions 59
Exponential 39 Practice Questions 59
Beta 40 Answers 60
Mixtures of Distributions 40 Short Concept Questions 60
3.3 Summary Solved Problems 60
43
Questions 44
Short Concept Questions 44 Chapter 5 Sample Moments 63
Practice Questions 44
Answers 45
Short Concept Questions 45 5.1 The First Two Moments 64
Solved Problems 45 Estimating the Mean 64
Estimating the Variance and Standard
Deviation 65
Presenting the Mean and Standard
Chapter 4 Multivariate Random Deviation 66
Variables 47 Estimating the Mean and Variance
Using Data 67
5.2 Higher Moments 67
4.1 Discrete Random Variables 48
5.3 The BLUE Mean Estimator 70
Probability Matrices 48
Marginal Distributions 49 5.4 Large Sample Behavior
Independence 50 of the Mean 71
Conditional Distributions 50 5.5 The Median and Other Quantiles 73
iv ■ Contents
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