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Lecture 01

For today you should:
  1. Learn Python.  First homework will check where you are.
  2. Buy, borrow or steal the book.
  3. Sign up for the mailing list.  Include your name in the request.
  4. Read the project page.
Today:
  1. Overview.
  2. The Laws of Probability.
  3. Bayes Theorem.
For next time:
  1. Read Chapters 1 and 2.
  2. Do Homework 1. 
  3. Prepare a question/dataset pitch: what do you want to explore, where are you getting data?


Overview


Project-based approach.
  1. Textbook presents basic tools.
  2. You practice them on data from NSFG and other sources.
  3. You apply them to a question and a dataset of your choice.
  4. You will need to learn additional techniques, depending on your project.
Question/dataset suggestions are here.  

Collaborate?  Yes, if there are groups working on similar topics, but individual coding and project writeup.

Seven weeks is short!  See the schedule. You are going to need to carpe the heck out of this diem.

Grading:
  1. Homeworks, put code in Dropbox.  Mostly binary grading.
  2. Reading-reading-quiz.  In-class, ~45 minutes.
  3. Project: Complete writeup due at the end of the session, but I will look at drafts.


The girl named Florida problem


The following questions are adapted from Mlodinow, 

The Drunkard’s Walk.
    1. If a family has two children, what is the chance that they have two girls?
    2. If a family has two children and we know that at least one of them is a girl, what is the chance that they have two girls?
    3. If a family has two children and we know that the older one is a girl, what is the chance that they have two girls?
    4. If a family has two children and we know that at least one of them is a girl named Florida, what is the chance that they have two girls?

You can assume that the probability that any child is a girl is 1/2, and that the children in a family are independent trials (in more ways than one). You can also assume that the percentage of girls named Florida is small.


What's the point of this example?
  1. Drawing a space of outcomes, assigning probabilities.
  2. Defining conditional probability.
  3. Inferring the laws of probability.
Are children independent trials?

A few years ago, my cousin Susan was expecting her fifth child.  Her first four children were all boys.  What was the probability that the fifth would be a boy?


Bayes's Theorem


Let's warm up with a ubiquitous urn problem.  From Wikipedia:

Suppose there are two full bowls of cookies. Bowl #1 has 10 chocolate chip and 30 plain cookies, while bowl #2 has 20 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. We may assume there is no reason to believe Fred treats one bowl differently from another, likewise for the cookies. The cookie turns out to be a plain one. How probable is it that Fred picked it out of bowl #1?

What if we draw another cookie and it is also plain?

The M&M problem


The blue M&M was introduced in 1995.  Before then, the color mix in a bag of plain M&Ms was (30% Brown, 20% Yellow, 20% Red, 10% Green, 10% Orange, 10% Tan).  Afterward it was (20% Blue , 20% Green, 16% Orange, 14% Yellow, 13% Red, 13% Brown).

A friend of mine has two bags of M&Ms, and he tells me that one is from 1994 and one from 1996.  He won't tell me which is which, but he gives me one M&M from each bag.  One is yellow and one is green.  What is the probability that the yellow M&M came from the 1994 bag?


The Elvis Problem

from MacKay, "Information Theory, Inference, and Learning Algorithms."


Elvis Presley had a twin brother who died at birth.  According to the Wikipedia article on twins:

``Twins are estimated to be approximately 1.9% of the world population,
with monozygotic twins making up 0.2% of the total---and 8% of all
twins.''

What is the probability that Elvis was an identical twin?

If this is your idea of fun, there are more on Probably Overthinking It.

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