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#1 2011-06-20 22:09:56
- lindah
- Member
- Registered: 2010-01-25
- Posts: 121
Point Estimates
Hi Guys,
I am attempting another question for my exam as follows:
http://imageshack.us/photo/my-images/32/48188946.png/
For Q1) I used the following limits for my integral
Q2) My final answer is:
Q3) My answer after solving the derivative of the log likelihood
Thank you in advance
Linda
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#2 2011-06-20 22:38:50
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Point Estimates
Hi lindah;
Q1) The integration looks okay and I agree with the interval you chose.
How did you get Q2?
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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#3 2011-06-20 22:49:53
- lindah
- Member
- Registered: 2010-01-25
- Posts: 121
Re: Point Estimates
Hi bobbym,
I first looked for the expectation of the integral from Q1
Then equating
Last edited by lindah (2011-06-20 23:29:38)
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#4 2011-06-20 22:53:21
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Point Estimates
Can I see a little bit more and do you need help with Mathematica?
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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#5 2011-06-20 23:31:00
- lindah
- Member
- Registered: 2010-01-25
- Posts: 121
Re: Point Estimates
Hi bobbym,
I've updated post#3 to expand on it a bit.
w.r.t to Mathematica, not at the moment (I seem to have made a rookie mistake), however thank you for asking!!!
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#6 2011-06-20 23:53:37
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Point Estimates
Hi;
Looks okay to me. I just hope we are not both wrong.
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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#7 2011-06-21 00:29:44
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Point Estimates
Hi,
Looks okay to me too.
I'm new to MLE, here's my attempt, I'm using notation from http://mathworld.wolfram.com/MaximumLikelihood.html
Is it okay?
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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#8 2011-06-21 02:55:36
- lindah
- Member
- Registered: 2010-01-25
- Posts: 121
Re: Point Estimates
Hi gAr,
I think yours is correct as it maintains the sum notation throughout.
I should do it your way, as I initially obtained the same MLE as you before canceling out the "n's" - which I shouldn't have since n and sigma notation are different in this case
I had
Thank you both for your feedback and sharing!!!
Last edited by lindah (2011-06-21 02:55:51)
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#9 2011-06-21 03:01:20
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
Re: Point Estimates
Hi lindah,
You're welcome.
But I'm not very sure since it's my first problem on MLE.
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
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