Hi Bob,
I imagine you're probably not alone in being a little confused! Maybe I can
help with the intuition behind the integral stuff. So (and I'm taking some
of this language from Wikipedia), remember that the PDF is a function that
describes the relative likelihood for the random variable to occur at a
given point in the observation space. In non-mathy terms, the PDF basically
tells you what the random variable's distribution is (i.e, how the random
variable behaves). Statisticians have derived the PDFs for a lot of
well-known, commonly occurring continuous distributions, such as the Normal
distribution, the t distribution, the uniform distribution, the exponential
distribution (which we talked about in section), etc.
Once you have the PDF of a random variable X, you can then move forward and
calculate different things with it. For example, if you want to calculate
the expected value of X (a.k.a., its mean), then you can use the following
formula
[image: \operatorname{E}(X)=\int_{-\infty}^\infty x\,f(x)\,dx.]
where f(x) is the PDF of the random variable X. All the integral is saying
here is that you are taking the area underneath that particular curve --
which is x*f(x) -- from minus infinity to positive infinity.
Similarly, if you want to calculate the probability that your random
variable X is between points "a" and "b", then you also use the
integral of
the PDF as follows
[image: \operatorname P [a \leq X \leq b] = \int_a^b f(x) \, \mathrm{d}x .]
All that's saying is that you take the area under the curve created by the
PDF bounded by points "a" and "b". Note that if "a" and
"b" are minus and
positive infinity, then this will be 1. (Ask yourself why that is for a
sanity check.)
I hope that helps with the intuition a little bit. One of the nice things
about using simulation techniques is that it lets you avoid having to work
with nasty integrals. But many of the simpler PDFs, you can try to integrate
(i.e., calculate the area under the curve) using basic rules of calculus.
If you're getting stuck on trying to remember the rules of calculus, then
I'd recommend spending an hour or so with a calculus study guide. One book
that some of my friends have liked is a book called "Quick Calculus: A
self-teaching guide." I think it's like $15 on Amazon.
But, again, keep in mind that one of the points of this class is to get you
using simulation techniques so that you can work with very messy PDFs quite
easily.
hope that helps, and please don't hesitate to ask more questions!
Maya
On Fri, Jan 29, 2010 at 12:27 PM, Bobby L. Woods <blwoods at fas.harvard.edu>
wrote:
2:30 is good for me also. At the risk of really embarrassing myself I like
to
ask if anyone else found the whole integral calculus
techniques a bit
confusing
in last nights section? I vaguely remember the
concepts from way back in
the
day.
Bob
Quoting Niroshika Silva <niroshika at gmail.com>:
> Sunday at 2.30 is good for me ...
>
> niroshika
>
> On Thu, Jan 28, 2010 at 7:46 PM, Meryl Federman
> <federman at fas.harvard.edu>wrote:
>
> > Ah, brilliant, my computer just wasn't seeing it, but it was there.
> > Awesome. And yes, Sunday at 2:30 works for me for going forward.
> >
> > ~Meryl
> >
> > On Jan 28, 2010, at 7:37 PM, Han He wrote:
> >
> > Hey, anyone want to work on problem sets on Sunday afternoon at Lamont
> > Cafe?
> >
> > Han
> >
> > On Thu, Jan 28, 2010 at 7:15 PM, Meryl Federman
> <federman at fas.harvard.edu>wrote:
> >
> >> There isn't a problem set posted yet, right? I am just hoping that
I'm not
> >> missing anything...
> >>
> >> ~Meryl
> >>
> >> On Jan 28, 2010, at 5:07 PM, Yousuf wrote:
> >>
> >> Dear Han: It would be helpful if you listed a time and a place for
people
> >> to meet. Perhaps a saturday or a sunday
might work for most.
> >>
> >> YM
> >>
> >> On Thu, Jan 28, 2010 at 4:42 PM, <
> >> gov2001-l-request at lists.fas.harvard.edu> wrote:
> >>
> >>> Send gov2001-l mailing list submissions to
> >>> gov2001-l at
lists.fas.harvard.edu
> >>>
> >>> To subscribe or unsubscribe via the World Wide Web, visit
> >>>
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> >>> or, via email, send a message with subject or body 'help' to
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> >>>
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> >>> When replying, please edit your Subject line so it is more specific
> >>> than "Re: Contents of gov2001-l digest..."
> >>>
> >>>
> >>> Today's Topics:
> >>>
> >>> 1. Re: Work Buddies (Han He)
> >>> 2. Re: gov2001-l Digest, Vol 54, Issue 3 (Yousuf)
> >>> 3. Re: gov2001-l Digest, Vol 54, Issue 3 (Lin, Eric)
> >>> 4. first section reminder (Maya Sen)
> >>>
> >>>
> >>>
----------------------------------------------------------------------
> >>>
> >>> Message: 1
> >>> Date: Thu, 28 Jan 2010 16:17:14 -0500
> >>> From: Han He <han.he at college.harvard.edu>
> >>> Subject: Re: [gov2001] Work Buddies
> >>> To: "Class List for Gov 2001/E-2001" <
gov2001-l at
lists.fas.harvard.edu>
> >>> Message-ID:
> >>> <65368ef21001281317x4b90f738jd2f307a49452cd2f at
mail.gmail.com>
> >>> Content-Type: text/plain; charset="iso-8859-1"
> >>>
> >>> I am totally open to grad students too, although meeting together
might
> >>> be
> >>> more difficult.
> >>>
> >>> Han
> >>>
> >>> On Thu, Jan 28, 2010 at 11:32 AM, Niroshika Silva <
niroshika
at
gmail.com
> >>> >wrote:
> >>>
> >>> > I would like to work together for the problems....
> >>> >
> >>> > niroshika
> >>> >
> >>> >
> >>> > On Thu, Jan 28, 2010 at 1:11 AM, Meryl Federman <
> >>> federman at fas.harvard.edu>wrote:
> >>> >
> >>> >> Yes!
> >>> >>
> >>> >> ~Meryl
> >>> >>
> >>> >> On Jan 28, 2010, at 1:05 AM, Han He wrote:
> >>> >>
> >>> >> > Hey, are there any undergrads that would like to work
together
for
> > >>> >> > problems, etc?
> > >>> >> >
> > >>> >> > Best,
> > >>> >> > Han He
> > >>> >> > _______________________________________________
> > >>> >> > gov2001-l mailing list
> > >>> >> > gov2001-l at
lists.fas.harvard.edu
> > >>> >> >
http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l
> > >>> >>
> > >>> >> _______________________________________________
> > >>> >> gov2001-l mailing list
> > >>> >> gov2001-l at
lists.fas.harvard.edu
> > >>> >>
http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l
> > >>> >>
> > >>> >
> > >>> >
> > >>> > _______________________________________________
> > >>> > gov2001-l mailing list
> > >>> > gov2001-l at
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> > >>> >
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> > >>> >
> > >>> >
> > >>>