## 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

Jim Mahoney (mahoney@marlboro.edu)