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jamesmartinn
07-08-2010, 12:36 PM
Hello all!

I have sort of a weird question / request.

I'll be taking Mathematical Statistics I and II come Sept and I really want to brush up on some areas. I've already done some reading into the subject and I've identified my weaknesses and was hoping to get some help or direction with specifically with integration and associated properties of common densities.

To be more clear, take the Gamma density for example. It's daunting. I'm a bit rusty in integral calculus and will most likely have problems with questions that require the integration of such densities to find probabilities, show results and perform transformations.

So, what I'm asking is whether or not someone has a DOC/PDF/course lecture or some kind of aid that I can use to get acquainted with the calculus of common probability densities.

I was able to locate this document: http://www.docstoc.com/docs/2583168/Stat-134-Fall-2008-A-Adhikari-GAMMA-DENSITIES-STEP-BY-STEP

I'd really appreciate if anyone had a resource that takes this kind of approach: step-by-step.

I know it's a bit of a weird question, but I'm confident that this is indeed a weakness in my education that I'd like to improve. I've tried googling a ton of queries and have only turned up a small amount of useful results.

TIA

Dason
07-08-2010, 01:45 PM
Do you know what book you'll be using? That'd be a good place to start. But I wouldn't worry too much. You'll learn most of the stuff you'll need during the class.

jamesmartinn
07-08-2010, 02:06 PM
Hey Dason, thanks for the reply.

I'll be using this text:http://www.amazon.com/Mathematical-Statistics-Chapman-Statistical-Science/dp/158488178X

I'm in a bit of a weird situation.

In Sept, I'll be starting my MSc in biostatistics and Math Stats I and II are two courses I'll have to complete. My problem: My undergrad is in Psych with a significant emphasis on applied methods (generalized linear models, multivariate models, SEM, etc), and while I have taken some more theoretical courses (elementary probability, sampling design, etc) I haven't taken the undergrad version of Math Stats I and II. I've done a lot of reading myself to play catch up, but theres still a few gaps I need to bridge. I feel a bit unprepared to be honest, but I know I'll be able to do well If I prep a lot in advance. I've been brushing up on calc, multivariable calc and some linear algebra.

Right now I have a strong aversion to any kind of integral with exp in it LOL!

Any resources / tips are appreciated!

Cheers!

mp83
07-08-2010, 02:54 PM
I only have a book to propose "Advanced Calculus with Applications in Statistics"

http://www3.interscience.wiley.com/cgi-bin/bookhome/104086617?CRETRY=1&SRETRY=0

However google can help you find a "note"-ish version of the subject.

Dason
07-08-2010, 10:18 PM
Right now I have a strong aversion to any kind of integral with exp in it LOL!

Oh sad. Those are my favorite kind ;) (as long as you're integrating from 0 to infinity) The trick is usually to play with it until you get in the form of a gamma kernel (might end up being a special case like the exponential or the chisquare but it's all the same) and then walla! You're gold. That probably wasn't too much help though and sometimes you need to do a transformation first.

Ok, they can be tricky but a lot of times if you can get it into the form of
x^{something}exp(-x/(somethingelse)) then you're good to go because we know what that integrates to.