Just posted a similar thread, but I'm not sure if you're allowed multiple questions in one thread (sorry if you are!)

$\displaystyle X$ is exponentially distributed with parameter $\displaystyle \lambda$. For the random variable $\displaystyle Y=\frac{1}{X}$

i) State the range of values $\displaystyle Y$ can take.

ii) Obtain the distribution function of $\displaystyle Y$, $\displaystyle F_{Y}(y)$.

iii) Obtain the probability density function of $\displaystyle Y$, $\displaystyle f_{Y}(y)$.