Statisticians_group : Message: Re: [Statisticians

Hi Kaushik,

Thanks for your suggestion. I have both the books but I could not find the solution there. Anyway, I have solved my problem. Please find the solution in the attachment.

Anyway I would like to see the solution from Shiryaev (Probability), if it does have. I don't have the book. I want to have this book hoping that it will make me more comfortable with the topic of convergence. Please send me the details of the book.

--------------

Madan Gopal Kundu
PhD Scholar
Indiana University Purdue University Indianapolis (IUPUI)

Indianapolis, Indiana 46202, USA

Web: http://mgkundu.webs.com/

Cell: 317-657-1180 317-657-1180

Sir Ronald Aylmer Fisher: "To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of."

Roger Brinner: "The plural of anecdote is not data."

John Tukey: "The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data."

--- On Mon, 19/10/09, KAUSHIK BHATTACHARJEE <kabonline07@...> wrote:

From: KAUSHIK BHATTACHARJEE <kabonline07@...>
Subject: Re: [Statisticians_group] Convergence problem
To: Statisticians_group@...
Date: Monday, 19 October, 2009, 2:07 AM

Most probably Rohatgi's book .Mathematical Stat or Hogg& Craig's book

Pls let me know ...else Shiryaev (Probability) will definitely have...

Kaushik Bhattacharjee

--- On Sat, 10/17/09, Madan Kundu <madan4331@yahoo. co.in> wrote:

From: Madan Kundu <madan4331@yahoo. co.in>
Subject: [Statisticians_ group] Convergence problem
To: statisticians_ group@yahoogroup s.co.in
Date: Saturday, October 17, 2009, 2:26 PM

Hi,

I have following problem to solve:

Let X(n) be a sequence of random variables and X(n) converges in distribution to X where X follows Normal distribution with mean Mu and variance sigma square. I have to prove that X(n) is bounded in probability.

This means I have limF[X(n)] = F(X) and I need to prove that for every, e>0, there exist M for which P[|X(n)| > M] < e for all n.

Please suggest me where I can get this solution.

Thanks & Regards.

Madan Gopal Kundu

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