Consider an exponentially$-$distributed random variable $x$ with $PD{F}_x(x)=2$exp$(-2x),x>0$

Assume two RVs $Y$ and $Z$ are given by the transformations: $Y=ln(x),$ and $Z=x^2.$

a$)$ Find the PDF of $Y$

b$)$ Find the PDF of $Z$

c$)$ Are $Y$ and $Z$ independent? Explain.