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The exact answer is:
Seems pretty good. Try for larger n with x small in comparison to convince yourself numerically.
I think the limit is 1.
According to M that is true. Why do you think the limit is not 1?
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.
Ok, I will try to think about it a bit. Thanks a lot.
I am not getting how you get that...
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.
Can you prove it then?
Post 7 is what I need proven/
That is what the original problem is asking for. But I cannot get it. I am using the limit definition and Stirling's formula.
that I can prove.
How do you do that?
It does seem to work without the minus sign, though.
I do not think so either.
I don't think that would be correct, then.