SIG Quantitative Researcher Interview Question: Expected Value of a Uniform Random Variable
Quantitative researcher interviews at firms like Susquehanna International Group (SIG) are known for their rigorous mathematical and probability-based questions. One classic problem that tests both your mathematical intuition and technical skills is computing the expected value of a function of a random variable, particularly when the variable is uniformly distributed. In this article, we’ll delve deeply into the question: “Let \( X \sim \text{Uniform}(0,1) \). Compute \( \mathbb{E}[X^3] \).” We will not only solve the problem step by step, but also explore the underlying concepts, variations, and practical implications relevant to quant research interviews.
Before solving the problem, it’s essential to understand the core concepts behind the uniform distribution, which is one of the most fundamental probability distributions in quantitative finance, statistics, and probability theory.
A random variable \( X \) is said to follow a continuous uniform distribution on the interval \([a, b]\), written \( X \sim \text{Uniform}(a, b) \), if it has a constant probability density function (PDF) over that interval.
