Maximum of Geometric Variables Asymptotic Expectation - Quant Trader Interview Question
Difficulty: Hard
Category: Probability & Statistics
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Topics: probability, expected-value, asymptotics, geometric-distribution
Problem Description
You are tasked with analyzing the potential upside of a new options trading strategy. The strategy's profitability in any given day can be modeled as a Geometric random variable representing the number of successful trades before the first failure, with a daily success probability p. You want to estimate the expected maximum daily profit over n trading days. Assume daily profits are independent and identically distributed.
Let $X_1, X_2, ..., X_n$ be i.i.d. Geometric random variables with succ
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