For each of the following statements related to Simulation, state whether it is true or false. Justify, in no more than three lines, whichever is the case.

a$)$ Consider the following function f$($x$)=$ x$*$e$^$x$,$ x in $[0,100].$ Suppose you want to generate instances of a random variable that distributes according to f$($x$).$ The best method to generate instances of this random variable is the inverse transform.

b$)$ Consider the diagram in figure $1($Graphic results simulation$).$ If you want to perform an analysis of the results of a simulation in steady state, you must consider the complete interval t in $[0,200].$

c$)$ In a study, the behavior of two machines A and B has been simulated, to measure the operating time of both. After $100$ replications, the average time for machine A was $5\mathrm{.}11$ minutes, while for machine B it was $5\mathrm{.}04$ minutes. From this, it can be statistically declared that machine A is better than B$.$