Tues Sep 18 - Statistics Lecture Notes

• questions

• Hand back homework.

• Discuss class survey; show compilation of results.

• Continue discussion of probability; do a few examples.
  • The most important part is the underlying idea; counting things can get messy in any particular example.
  • How many people before 50/50 chance that 2 have same birthday?
  • A couple has 5 children. What is the probability that 2 are boys and 3 are girls?
  • What are the odds of being dealt a 5 card flush ? Two aces? A pair of any kind?
  • You picked door number 1. But wait - what if I say that ...
  • Which is more likely, being killed in a car accident or being killed in a plan crash? How would you find out?
• Revisit formula for mean in terms of probabilities : "expected value".
  • chuck-a-luck: roll 3 die, pick a number. You win : $3 if your number is on all 3; $2 if your number is on 2; $1 if its on one. If your number doesn't come up, you pay $1. Is this a fair game? Which side would you rather play? How much would you make in the long run?
  • Lottery: how do you calculate an "expected value"? And what does that number really mean?
  • St Petersberg paradox, and its various resolutions.

• Common sense
  • stock market scam
  • pg 40 in innumeracy; court case

• Try to displaying class survey data with Excel

• Start talking about binomial distribution (chap 5)
  • "bi" - system with 2 values
  • p = probability of "success"
  • q = 1- p = probablity of "failure"
  • n = number of trials
  • S = total number of successes
  • example on pg 129: lung cancer patients
  • C(n,m) = number of ways a subset of m things can be taken from a group of n
    = "binomial coefficient"
    = n!/( m! (n-m)! )
    = number in Pascal's triangle
  • some examples from end of chap 5