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bobbym
2013-06-22 21:43:39

yields 0.001079819330263761

yields 0.0010798643294

Seems pretty good. Try for larger n with x small in comparison to convince yourself numerically.

#### anonimnystefy wrote:

Have you tried getting the limit of the ratio of the two expressions (the exact one and the approximate one)? It does not approach 1.

I think the limit is 1.

According to M that is true. Why do you think the limit is not 1?

#### bobbym wrote:

To prove that you might need the limit but maybe since Stirlings formula is asymptotic to the factorial it might be implied in step 3.

Stirlings is an asymptotic form for the factorial. The limit of the ratio of Stirlings and the factorial is 1. The fact that he use Stirlings in his proof guarantees the above limit.

anonimnystefy
2013-06-22 21:34:59

Hi bobbym

Have you tried getting the limit of the ratio of the two expressions (the exact one and the approximate one)? It does not approach 1.

ShivamS
2013-06-22 10:00:03

Ok, I will try to think about it a bit. Thanks a lot.

bobbym
2013-06-22 03:44:15

Hi Shivamcoder3013;

I am not getting much of the derivation either. It is a lot of algebra and undoubtedly was done with the help of a package. I put it down so you would have something.

ShivamS
2013-06-22 02:19:52

I am not getting how you get that...

bobbym
2013-06-21 11:48:02

Hi;

The paper I am looking at "Gaussian and Coins."

Using Stirlings:

Notice the approximately equal sign that is because you are approximated a discrete distribution ( binomial ) with the Normal distribution.

1) is an approximation for 2) which the above steps prove. Even for large N it is still an approximation. When N approaches infinity 1) = 2).

To prove that you might need the limit but maybe since Stirlings formula is asymptotic to the factorial it might be implied in step 3.

anonimnystefy
2013-06-21 10:10:35

Hi Shivamcoder3013

Have you tried taking the limit as N goes to infinity of the ratio of the exact answer and the approximate one and proving it equals 1?

ShivamS
2013-06-21 04:47:59

Can you prove it then?

ShivamS
2013-06-19 09:53:45

Post 7 is what I need proven/

anonimnystefy
2013-06-19 08:15:17

That is what the original problem is asking for. But I cannot get it. I am using the limit definition and Stirling's formula.

bobbym
2013-06-19 02:22:35

Hi;

Do what?

that I can prove.

Agnishom
2013-06-19 02:18:19

How do you do that?

anonimnystefy
2013-06-19 02:12:58

It does seem to work without the minus sign, though.

bobbym
2013-06-19 02:04:07

I do not think so either.

anonimnystefy
2013-06-19 01:52:44

I don't think that would be correct, then.