Jane Street Quant Interview: Expected Value in 10-Sided Dice Game
The Jane Street Quantitative Researcher interview is renowned for its challenging probability and statistics problems. A classic example involves calculating the expected value in games of chance, such as those featuring dice. In this article, we will analyze a well-known interview question involving a fair 10-sided die, exploring the required concepts, step-by-step solutions, and practical implications. This comprehensive guide will not only help you approach such questions in interviews but also deepen your understanding of expected value and related quantitative reasoning skills.
Suppose you are presented with a fair 10-sided die, with faces numbered from 0 to 9. The die is rolled once, and your payoff depends on the outcome according to certain rules. The interviewer asks you:
Let’s break down the question, analyze the scenario, and provide a detailed solution. Along the way, we will explain key probability concepts, the notion of expected value, and several variations of payoff rules commonly encountered in quant interviews.
