Assume Xn~GAM(1,n) and let Zn=(Xn-n)/sqr(n). Show that Zn converges in distribution to Z~N(0,1).
Hint: Show that Mzn(t)=exp(-sqr(n)*t - ln(1-t/sqr(n))) and then use the expansion ln(1-s)=-s-(1+E)s^2/2 where E->0 as s->0.
Does the above limiting distribution also follow as a result of the CLT? Explain your answer