Suppose $\displaystyle X$ has density $\displaystyle f_X (x) = \frac{ba^b}{x^{b+1}}$ if $\displaystyle x>a>0,$ otherwise $\displaystyle f_X (x)=0$

$\displaystyle (a)$Describe how to sample from this distribution using the method of inversion.

$\displaystyle (b)$Find the MLE estimates for $\displaystyle a$ and $\displaystyle b$ from $\displaystyle n$ $\displaystyle i.i.d.$ samples.

$\displaystyle (c)$Determine the asymptotic variance of the MLE estimates.