Challenging Stats Questions - Help appreciated

Hi guys,

Any help will be much appreciated on these questions:

1.

Let

*X*1*;X*2*; : : : ;Xn *be a random sample from a Pareto distribution which has

probability density function

f

(*x*) = 1/[(1 + *x*)^2] *x > *0*:*

Find the limiting distribution of *Yn *= *nX*(1).

2.

[SIZE=1][FONT=CMR10]Let

*X*1*;X*2*; : : : ;Xn *be a random sample from a distribution which has probability

density function

f

(*x*) = *e^[-x-µ*] *x > µ:*

Find both the moment estimator and the maximum likelihood estimator of the

parameter *µ*.