The Jacobian Transform - Quant Trader Interview Question
Difficulty: Hard
Category: Probability & Statistics
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: probability, jacobian, transformation, normal-distribution
Problem Description
Let $X$ and $Y$ be independent and identically distributed (i.i.d.) standard normal random variables. Define new random variables $R$ and $\Theta$ such that $X = R \cos{\Theta}$ and $Y = R \sin{\Theta}$. Find the joint probability density function (PDF) $f(r, \theta)$ of $R$ and $\Theta$.
Practice this hard trader interview question on MyntBit - the all-in-one quant learning platform with 200+ quant interview questions for Jane Street, Citadel, Two Sigma, and other top quantitative finance firms.