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#26 2011-09-14 06:41:29
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Urgent help - Easy differentiation problem!
I might not have done a) that way.
As you can see I can keep dividing terms out until gibberish is produced. Without knowing about those constants I do not know whether I am dividing out by 0.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#27 2011-09-14 07:42:51
- anony
- Guest
Re: Urgent help - Easy differentiation problem!
Oh dear. I see what you mean.
How would you do it then?
#28 2011-09-14 07:46:39
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Urgent help - Easy differentiation problem!
Hi;
I do not see any way to do it. It might not be possible. Since this is a school problem it is unlikely that you would be unable to isolate p,
That might mean you are minimizing the wrong equation.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#29 2011-09-14 07:48:24
- anony
- Guest
Re: Urgent help - Easy differentiation problem!
In that case I simply end up with:
And I can't go further.
#30 2011-09-14 07:49:39
- anony
- Guest
Re: Urgent help - Easy differentiation problem!
I see.
Anyway thank you very much for the help 
#31 2011-09-14 07:50:50
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Urgent help - Easy differentiation problem!
Hi;
Good luck and let me know if it does not turn out the way you want. Welcome to the forum!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#32 2011-09-14 10:49:30
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,583
Re: Urgent help - Easy differentiation problem!
hi anony,
Sorry for the late contribution. I've been out all day fixing my Mum's garden.
I started at post #5 and got
Binomials are approximately normal distributions so differentiating will lead to the maximum point.
You would graph P against Ni for this.
If you treat Ni as constant and Pi as a variable you get
which is what you had at post #18.
Those n C ni occur in both terms and, since they won't be zero, can be cancelled out harmlessly.
But I cannot see why this treatment of Ni is valid, so I'm going to have another think about this. Back when I've got something useful to say ......
...........later
OK. I've had a think.
The differentiation is impossibly nasty if Ni is treated as a variable throughout.
Also, in that formula what happens if Ni is less than half of N .... Pi cannot be negative, so that formula must be wrong!
The maximum point on the graph is the expected value of Ni, which is also given by Pi.N (standard binomial theory)
So, do we have to do differentiation at all? Assume that the maximum is at Ni; then:
Can it really be this simple?
Well, why not?
We only have a single sample so our best estimate for Pi is the 'experimental probability' which is Ni/N
So that's what I'm going for.
Bob
Last edited by Bob (2011-09-14 20:51:06)
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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