Create an R script with the following components:

$$ Create a function to prove the Central Limit Theorem using a given equation. This function will be used in future week's assignments.

$$ Create a function to perform a quick sort.

$$ Create a binary search tree function.

$$ Create a discrete event simulation for a queue system involving a bus terminal. It should include an event list, along with components to add and subtract from that list as buses arrive and depart from the terminal. The following functions should be present:

$$ Core simulation function

$$ Variable initialization

$$ Add event

$$ Event response

$$ Get next event

$$ Function to print the results of the simulation