Probability Distributions and Hypothesis Testing
The statistical foundations every FRM candidate must master: normal, lognormal, t-distributions, confidence intervals, and Type I/II errors.
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Volatility Clustering Intuition
Returns can look calm for a while and then surge into high-volatility pockets. This is the intuition behind time-varying volatility models.
Why it matters
Quant questions often test whether you understand persistence and clustering, not just a memorized formula.
Probability Distributions and Hypothesis Testing
Key Distributions for FRM
The FRM exam expects you to work fluently with several probability distributions. You must know their properties, when to use each, and how to interpret parameters.
Continuous Distributions
| Distribution | Key Parameters | FRM Application |
|---|---|---|
| Normal | μ (mean), σ (std dev) | VaR calculations, return modeling |
| Lognormal | μ, σ of underlying normal | Asset price modeling (prices can't go negative) |
| Student's t | ν (degrees of freedom) | Small-sample testing, fat tails |
| Chi-squared | ν (degrees of freedom) | Variance testing, goodness-of-fit |
| F-distribution | ν₁, ν₂ | Comparing two variances, ANOVA |
Discrete Distributions
| Distribution | Key Parameters | FRM Application |
|---|---|---|
| Binomial | n (trials), p (probability) | Default counting, pass/fail outcomes |
| Poisson | λ (rate) | Operational loss frequency, rare events |
The Normal Distribution
The normal (Gaussian) distribution is the single most important distribution in risk management. Its properties:
- Symmetric around the mean μ
- Fully described by two parameters: μ and σ
- **68-95-9
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