QUICK REVIEW: RANDOMNESS AND
PROBABILITY (PART IV)
- LAW OF LARGE NUMBERS (LLN)
- more times we try sth, closer the results will get to theoretical perfection
- LAW OF AVERAGES DNE
BASIC RULES OF PROBABILITY
HOW TO FIND PROBABILITY OF: "this event OR this event occurs"?
- add probab's and subtract probab. that both occur
HOW TO FIND PROBABILITY THAT: "event A and event B" occurred, given they are
- multiply probab's
CONDITIONAL PROBABILITY: how probable is one event to happen, knowing that
another event happened
- ie. P(event A | event B) => probability of event A,
DISJOINT EVENTS => "mutually exclusive"
- cannot both occur at same time
IF two events are INDEP,
then occurence of one does not change probab. of the other occurring.
PROBABILITY MODEL FOR RANDOM VARIABLE
- describes theoretical distrib. of outcomes
- expected value = mean of random var.
- add variances for sums or diff's of INDEP. random var's
- IF distrib. of qvar var. is unimodal & symmetric
- THEN can use normal model to estimate probab;'s
a) GEOMETRIC model to est. probab. of getting first success after certain # of
b) BINOMIAL model to est. probab. of getting certain #successes in finite # of
c) POISSON model to est. probab. of #occurrences of relatively rare phenomenon
- approximation to BINOMIAL model
BEGINNING OF PART V OF THE BOOK: FROM THE DATA
AT HAND TO THE WORLD AT LARGE
SAMPLING DISTRIBUTION MODELS
WHERE ARE WE GOING?
- will find out how much proportions from random samples will vary
- allows us to start generalizing from retrieved samples to popn
- WHO: Canadian adults
- WHAT: When to bring troops home
- WHEN: Apr 2007
- WHERE: Canada
- WHY: Public attitudes
- to what extent should we see prop's (ex. of ppl favouring early withdrawl of troops)
The following polls both were taken within a similar time frame
- ex. Angus reid poll randomly selected 1k Canadians and found 52% in favour of
troops being withdrawn early from war
- ex. Strategic Counsel poll randomly selected same amt of Canadians and found
64% in favour
- both of these were properly selected random samples, but their prop's are strikingly
- why sample proportions vary going from 1 sample to another?
- b/c samples are made up of diff. ppl
THE CENTRAL LIMIT THEOREM FOR SAMPLE PROPORTIONS