SOLVE IN RSTUDIO

$$ Question $2.$a $-$ What is the height of the triangle at its peak, such that it is a valid probability distribution? Save your answer in the variable height

$$ Question $2.$b $-$ Create a function area$\_$to$\_$the$\_$left, which takes a single variable $($x$1)$ and calculates the area to the left, returning a value between $0$ and $1.$ The basic setup of the function is defined in the provided code. Note that you will need to use a slightly different equation if x$1$ is less than or greater than $3.$

$$ Question $2.$c $-$ Create a function area$\_$to$\_$the$\_$right, which takes a single variable $($x$1)$ and calculates the area to the right, returning a value between $0$ and $1.$ The skeleton of the function is defined in the provided code. You can attempt to copy the setup used in the previous function, but students may find it easier to utilize area$\_$to$\_$the$\_$left$()$ already defined.

$$ Question $2.$d $-$ Create a function area$\_$between, which takes two numeric variables $($x$1$ and x$2)$ and calculates the area between them, returning a value between $0$ and $1.$ You can assume that x$1$ x$2.$ The skeleton of the function is defined in the code, and again students

may find it easiest to utilize the previously defined functions area$\_$to$\_$the$\_$left$()$ and$/$or area$\_$to$\_$the$\_$right$().$

$$ Question $2.$e $-$ If we generate a random number utilizing this distribution, what is the probability that we get a number less than $1$ or greater than $4$ Save your answer in the variable q$2.$e

$$ Question $2.$f $-$ If we generate a random number utilizing this distribution, what is the probability that we get a number between $2\mathrm{.}5$ and $3\mathrm{.}75?$ Save your answer in the variable q$2.$f

$$ Question $2.$g $-$ If we generate a random number utilizing this distribution, but we discard any value greater than $4,$ what is the probability that we get a value greater than $1\mathrm{.}5?$ Save your answer in the variable q$2.$g

$$ Question $2.$h $-$ If we generate two random numbers utilizing this distribution, what is the probability that one of the numbers is greater than $2\mathrm{.}5,$ and one is less than $2\mathrm{.}5?$ Save your answer in the variable q$2.$h