Assume xngam1n and let znxn-nsqrn show that zn converges in, Ask an Expert

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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

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M9982017

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