FRMⅠ- Part 2 - 定量分析Quantitive Analysis Ch1-2

FRM一级第二部分数量分析知识点总结： · Probability · Random Variables 持续整理更新，一起学习！

Quantitative Analysis (20%)

• Y - KEEP LEARNING - J
• Quantiles are always well-defined for any random variable
• Mode
  • Definition
    • mostly oberved values
  • Properties
    • A random variable may have zero or more than one modes
• Quantiles
  • Median
    • Definition
      • Measure of central tendency
  • Interquartile Range (IQR)
    • Definition
      • Difference between 75% and 25% quantiles
    • Propertities
      • Measure of dispersion.
      • Less sensitive to outliers.
• The Four Moments
  • Expectation
    • FRM一级不考连续型随机变量期望值的计算（需要用到积分），所以掌握离散型变量的期望计算的方法即可
    • Definition
      • The first non-central moment
    • Calculations
    • Properties
      • Doesn't pass through the nonlinear functions
  • Variance
    • Definition
      • The second central moment
    • Calculations
    • Properties
  • Skewness
    • FRM一级不考Skewness的计算，但定性要掌握
    • Definition
      • The third central moment
        • measures asymmetry in a distribution
    • Properties
      • skew[a+bX] = skew(X)
        • skew[a+bX] = -skew(X)
  • Kurtosis
    • Definition
      • The fourth central moment
        • measures the tail of distribution
    • Properties
      • Kurtosis[a±bX]=Kurtosis[X]
• Discrete Random Variables
  • Definition
    • Numbers of possible outcomes can't be counted.
  • Functions
    • Probability Density Function
    • Cumulative Distribution Function
• Discrete Random Variables
  • Definition
    • Numbers of possible outcomes can be counted.
  • Functions
    • Probability Mass Function
    • Cumulative Distribution Function
• Chapter 2 - Rndom Variables
• Probability Principles
  • P(A) ≥ 0
  • P(Ω) = 1
• Type of Probabilities
  • Unconditional Probability
    • P(A)
  • Conditional Probability
    • P(A|B)
  • Joint Probability
    • P(AB)
• Bayes' Rule
• Total Probability Theorem
  • A(j) are mutually exclusive and exhaustive.
• Event & Event Space
  • 该考点一般不考具体定义，结合已有教材理解即可，但要掌握不同事件的定义和数学表达及其之间的区别
  • Exhaustive Events
    • P(A+B) = 1
  • Mutually Exclusive Events
    • P(AB) = 0
  • Independent Events
    • A is independent to B, means P(AB) = P(A) * P(B)
• 2 Rules
  • Multiplication Rule
    • P(AB) = P(A|B)×P(B)
  • Addition Rule
    • P(A+B ) = P(A)+P(B)-P(AB)
• Machine Learning
• Simulation & Bootstrapping
• Return, Volatility & Correlation
• Time Series
• Regressions
• Hypothesis Testing
• Smaple Moments
• Distributions
• Random Variables
• Probability
• Chapter 1 - Fundamentals of Probability
• Chapter 1-2 | Start Date：2023/10/18 | End Date：2023/10/20 | Difficulty: ⭐⭐⭐