TL;DR
The bell curve distribution \( X \sim N(\mu, \sigma^2) \) with PDF \( f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-(x-\mu)^2/(2\sigma^2)} \). Fully characterized by mean \( \mu \) and variance \( \sigma^2 \).
Normal Distribution
The bell curve distribution \( X \sim N(\mu, \sigma^2) \) with PDF \( f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-(x-\mu)^2/(2\sigma^2)} \). Fully characterized by mean \( \mu \) and variance \( \sigma^2 \).
Why it matters for interviews
The default distribution in quantitative finance. Black-Scholes assumes log-normal returns, portfolio theory uses multivariate normals, and most statistical tests assume normality. Understanding when it fails (fat tails) is equally important.
Definition and Mathematical Foundation
The bell curve distribution \( X \sim N(\mu, \sigma^2) \) with PDF \( f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-(x-\mu)^2/(2\sigma^2)} \). Fully characterized by mean \( \mu \) and variance \( \sigma^2 \).
Application in Quantitative Finance
The default distribution in quantitative finance. Black-Scholes assumes log-normal returns, portfolio theory uses multivariate normals, and most statistical tests assume normality. Understanding when it fails (fat tails) is equally important.
Related Terms
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