the cheg AI answer is wrong. please help. write code for the project in R without using libraries:

Project$$s description

This is a little fun project, and short, too. The project aims to define a class that allows the creation of new probability distributions based on existing ones. The solution needs to be a S$3$ class named randomVariate. The constructor of the class must accept two arguments. The first one, named distFormula, should be a formula, e$.$g$.,$ ~ x $+$ y$,$ describing the function of one or more random variables. The second argument, named defs, should be a list of functions used for sampling from given distributions with keys corresponding to symbols used in the formula. The created object of the class randomVariate should be a function used for sampling from the distribution defined by the formula. You should also write the print method specific to this class. The following examples should clarify the concept. Following are output results of how the function should print outputs when it is called.

Example $1$

Let's start with a simple example. Let

be a standard normal random variable

$.$ The function used for sampling from this distribution in the R language is rnorm$().$ Suppose we want to define a new random variable

based on the random variable

$.$ Specifically, we want a function that allows for generating random numbers for this new random variable

$.$ We can define this new function using the constructor of the class randomVariate as follows.

### definition of the new variable

newDist $<-$ randomVariate$($

distFormula $=$ ~ x$^2,$

defs $=$ list$($

x $=$ rnorm

$)$

$)$

In the above snippet, we defined a new random variable

$.$ We used the constructor of the class randomVariate. The first argument of the constructor is a formula describing the function of the random variable

$.$ The second argument is a list defining the distribution of the random variable

$.$ Here, it is a standard normal distribution. The constructor creates a new object of the class randomVariate. We can print it out to see the mathematical definition of this new object.

newDist

Formula

~x$^2$

Definitions

x

$------------$

function $($n$,$ mean $=0,$ sd $=1)$

$.$Call$($C$\_$rnorm, n$,$ mean, sd$)$

The object is printed in a specific way. First, a formula is printed, and then all used definitions. Here, there is only one definition for the symbol x$.$ In this particular case, the definition is a function rnorm$(),$ which is just a call to a compiled function C$\_$rnorm$().$

We can use the new object as a regular function to sample random numbers from the new distribution. The following snippet creates a random sample and plots a histogram based on the sample.

sample$1<-$ newDist$(10^5)$

hist$($sample$1,$ breaks $=$ "Scott", probability $=$ TRUE,

col $=$ rgb$(1,0,1,\mathrm{.}2),$ density $=20,$ angle $=-45)$

lines$($

density$($sample$1,$ adjust $=\mathrm{.}5),$

col $=$ rgb$(1,0,1,1))$

The above snippet generates the following graph. The new variable takes only non$-$negative values.