(a) Starting from independent uniform random variables (U ~ Uni(0, 1)), devise an algorithm to generate independent samples from a Logistic distribution, having density f ( x) = for x E R (1 +ex)2' (b) Implement your sampling algorithm in R, and use your code to produce a Monte Carlo estimate of P(X E (2,3)) where X is a random variable that has a Logistic distribution. [Please note that using a function that already exists in an R library that samples from the Logistic distribution will not help you obtain any points for this question.]