User:Caliburn

b. 04/03/2001 from Kent.

My interest currently lies in complex analysis, which I've been studying using Gamelin, though I intend to broaden this.

2019 Cambridge offer holder. (Queens')

I prefer to be called by my real name, George, as opposed to Caliburn or any variation.

Statistics

 * Definition:Cauchy Distribution
 * Let $\theta \sim \ContinuousUniform {-\frac \pi 2} {\frac \pi 2}$. Let $X$ be the $x$-intercept of the line through $\tuple {x_0} \gamma$ that makes an angle of $\theta$ with the vertical line $x = x_0$. Then $X \sim \Cauchy {x_0} {\gamma}$.
 * Definition:Chi-Squared Distribution
 * Let $X_1, X_2, \ldots, X_n$ be iid standard normal. Then $\sum X_i^2 \sim \chi^2_n$.
 * Definition:Exponential Distribution
 * Let $T$ be the time period between consecutive events where these events happen at an average rate of $\lambda$. Then $T \sim \Exponential \beta$ with $\beta = 1/\lambda$.
 * Medians
 * Modes