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Hard · Probability & Statistics · Quant Trader interview question · probability, stochastic-calculus, brownian-motion, integral, variance
A quant trader is designing a novel trading strategy that relies on the properties of Brownian bridges. A key component of their model involves calculating the integral of a standard Brownian bridge. Let $B_t$ be a standard Brownian Bridge from 0 to 0 over the interval $0, 1$. What is the variance of the random variable $X = \int_0^1 B_t dt$?