Consider the Logistic diffusion process {X(t); t t0} with infinitesimal moments A1(x, t) = ab/(a+exp(x)) and A2(x, t) = ^2 x^2 conditioned to X(t0) = x0. In particular, consider the Logistic process in [0, 60] with parameters a = 10, b = 0.15 and = 0.001, and solve, making use of the fptdApprox package, the first-passage time problem of this process through the barrier S(t) = 0.1t^1.3 + 0.1 sin(1.4 t^0.55) conditioned to X(0) = 1: 1. Create a diffproc object that defines the family of Logistic diffusion processes. 2. Represent on the same graph the average of the process and the barrier for the considered problem. 3. Obtain and represent the graph of the FPTL function for the considered problem. Comment on its behavior and determine the time instants of interest that approach the first-passage time density. 4. Approximate the first-passage time density with variable integration step from the initial instant, and fixed integration step from the initial instant. Repeat the same approximation procedures but avoid applying the algorithm in any subinterval. Comment on the approximation procedures in each case: intervals where the algorithm is applied, integration steps, accumulated probability by the density, and computational cost (number of iterations and CPU time). Compare the computational cost of the different procedures and draw conclusions. Indicate the R code used to solve each section.