Modeling a Random Variable

Here are the javascript examples for Modeling a Random Variable, Section 13.4 in our text.  You can see the code for these examples by visiting these pages and selecting: View->Page Source from the menu in your Firefox browser.  I think it works the same for Internet Explorer and Safari.

http://www.nd.edu/~sbroad/30530SMR08/example-13-6.html

http://www.nd.edu/~sbroad/30530SMR08/example-13-7.html

“Immortal Monkey”

Here is a wikipedia entry that discusses the problem of a monkey typing forever and managing to type the collected works of Shakespeare.

http://en.wikipedia.org/wiki/Infinite_monkey_theorem

Law of Large Numbers

Here is a visual demonstration of the law of large numbers.  Oddly, it doesn’t actually explain what the law of large numbers is.  But it’s only five minutes long and has some interesting sound and visual effects.

http://video.google.com/videoplay?docid=-3278435881906648934

Central Limit Theorem example

Problem 11.5.2

Random sample with and .

We have been asked to compute .

But this is the same as .

We need to standardize.  If , then and .  So we have:

The z-score on the lower side is and the one on the upper side .

We can look up these z-scores in the tables, etc.  In the end what we get is as an approximate answer.

Mathematica examples

I have some example Mathematica files for you to try out.  I hope that it will make some of the computation easier.  Evaluate each block (called a “cell”) by typing “Shift+Return”.

Rather than clicking on the links, please right click (Ctrl-click for Mac users) and choose “save link as…” or whatever the equivalent in your non-Firefox web-browser is.

This one is basically the same as what I did in class:  http://www.nd.edu/~sbroad/30530SMR08/mathematica-9-1-7c.nb

This one is for the homework for 10.2 and 10.3.  Make sure that you evaluate the two blocks at the top of the file before you evaluate the rest of it:  http://www.nd.edu/~sbroad/30530SMR08/hw-10-2-10-3.nb

This one is for some of the examples that I did in class today:  http://www.nd.edu/~sbroad/30530SMR08/DeGroot-Central-Limit.nb

Homework Changes

I have changed the homework assignment for tonight and tomorrow night.  Please make note of the new assignment.

SAT I score statistics

Check out page 14.

http://www.collegeboard.com/prod_downloads/about/news_info/cbsenior/yr2004/2004_CBSNR_total_group.pdf

Functions on your calculator for normal distributions

On the TI-83, you have some capabilities that may save you some time on homework, quizzes and the final.

Select 2nd, VARS to get a list of probability related functions.  Two of these functions are especially useful: normalcdf and InvNorm.  You can see how to use them and what they do on the following webpage.

http://www.math.tamu.edu/~mpilant/math142/TI83-functions.html

Guidelines for exam corrections

1. Everyone (regardless of their score) is within reach of an ‘A’ if they put in the effort.
2. Please work on your exam corrections independently.
3. Please write your corrections on separate paper from the exam.
4. Please work out complete solutions to exam problems that you are correcting, even if they are multiple choice.
5. Please take your time.  You can make corrections a couple at a time and I will grade them incrementally.  If you prefer to do it all at once, that is also fine; but please don’t give me a boatload of corrections on July 31.  I need some time to go over them.
6. Please talk to me if you are stuck or don’t know what to do.  The goal of the exam corrections is not to make you feel bad, but to make sure that you understand the material.
7. You will not get credit for corrections that would move your score past the maximum score – 78 – for the exam.  However, if you like to talk about the solutions to problems that you missed, I am happy to do so.

Homework for Week Five…

…is now available.