Suppose the following statement is true for a continuous random variable $x$ :

$P\{xx\}=\frac{1}{1+x},x0$

Answer the questions below. $($You need to write the formulas you will use when answering. You also

need to use appropriate terminology and symbols. Write at least $4$ digits after the comma.$)$

a$)$ Find the cumulative distribution function of $x$ and draw a simple graph of it$.$

b$)$ Find the probability density function of $x$ and draw a simple graph of it$.$

c$)$ If a function of $x$ is given as $Y=x^2,$ find the probability density function of $Y.$