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Question 1: Short answer

mediumAI-checkedProbability

A Laplace random variable with mean 0 and variance 1 has density p(x)=12e−2∣x∣p(x) = \frac{1}{\sqrt 2} e^{-\sqrt 2 |x|}. You generate a sample by inverse transform sampling from u=0.9u = 0.9. Which value x=F−1(0.9)x = F^{-1}(0.9) do you get?

a number, 3 decimals