Question: [20 points]

1. [10 points] Starting from independent uniform random variables ( \(U\tilde{\ }Uni\left( 0,1 \right)\) ), devise an algorithm to generate independent samples from a Logistic distribution, having density
   \[f\left( x \right)=\frac{{{e}^{-x}}}{{{\left( 1+{{e}^{-x}} \right)}^{2}}}\] , for \[x\in \mathbb{R}\]
2. [10 points] Implement your sampling algorithm in R, and use your code to produce a Monte Carlo estimate of \(\Pr \left( X\in \left( 2,3 \right) \right)\) where X is a random variable that has a Logistic distribution.

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Deliverable: Word Document