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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

5 votes
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comparing Gaussian to order statistic of Gaussian

I would like to compute the probability of $$\mathbb{P}[Y > \max(X_i)], Y\sim N(0, 1), X_i \sim N(0, \sigma_i)$$ All the random variables have zero mean, but the variances are different. My approaches …