Announcements for Math 60, Spring 2012

Due dates of assignments and projects; exam dates:

http://www.math.dartmouth.edu/%7Edoyle/docs/60.2012/dates/dates.html

Tuesday 27 March

For Wednesday 28 March

Matlab

Get Matlab installed and running, and bring your laptop to the X-hour Wednesday. The link to download it is here:

http://caligari.dartmouth.edu/downloads/matlab/

Remember that to download and run these programs, you must be on the Dartmouth campus network, either via ethernet, Dartmouth Secure wireless, or VPN:

http://www.dartmouth.edu/comp/internet/offcampus/vpn/juniper.html

If you're new to Matlab, see if you can locate some Matlab-savvy person to pester for help.

Check out Alex Barnett's `bare essentials of Matlab':

http://www.math.dartmouth.edu/%7Em46s09/intro46.m

Look here for some simple probability demonstrations in Matlab:

http://www.math.dartmouth.edu/%7Edoyle/docs/60.2012/matlab/ch1/prob.m

How to count

Start reading the handout from class and see have far you can get. In particular, look at problems 6, 13, 16, 21, 23, 25, 27c. These won't be due until next Tuesday but look at them now.

The course text

Get hold of a copy of Grinstead and Snell's `Introduction to Probability', available at Wheelock Books. This book is available for free download on the web, but I guarantee you'll want a printed copy. This is a great book!

Take a look at section 1.1 of G&S (Grinstead and Snell), and specifically at exercises 1-5, 10, which will be due next Tuesday.

Mathematica

You might want to download Mathematica:

http://caligari.dartmouth.edu/downloads/mathematica/

Tuesday 24 April

I've been relying on email for announcements, without trying to keep this list current. I know I will regret this later on.

Here is the practice test we generated in class today: http://www.math.dartmouth.edu/%7Edoyle/docs/60.2012/t2p.pdf

Tuesday 15 May

Here's an alternate approach to computing the expected value of the sample variance

S² = $${\frac{{1}}{{n}}}$$$$\sum_{i}^{}$$E((X_i - $$\bar{{X}}$$)²),

where X₁,..., X_n are i.i.d. random variables with mean $\mu$ and variance $\sigma^{2}_{}$, and

$$\bar{{X}}$$ = $${\frac{{1}}{{n}}}$$$$\sum_{{i=1}}^{n}$$X_i.

1. Assume first that $\mu$ = 0.
2. Show that
   E((X₁ - $$\bar{{X}}$$)²) = E($${\frac{{(n-1)X_1-X_2-\ldots-X_n}}{{n}}}$$) = $${\frac{{(n-1)^2}}{{n^2}}}$$$$\sigma^{2}_{}$$ + (n - 1) ^. $${\frac{{1}}{{n^2}}}$$$$\sigma^{2}_{}$$ = $${\frac{{n-1}}{{n}}}$$$$\sigma^{2}_{}$$.

3. Conclude that
   E(S²) = $${\frac{{n-1}}{{n}}}$$$$\sigma^{2}_{}$$

4. Now either modify the argument to do without the assumption $\mu$ = 0, or argue that we can assume that $\mu$ = 0 `without loss of generality'.