Class Notes (1,100,000)
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Ken Butler (30)
Lecture
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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
independent.
 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,
given
event B
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.
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PROBABILITY MODEL FOR RANDOM VARIABLE
 describes theoretical distrib. of outcomes
 expected value = mean of random var.
 E(X)
 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
 use:
a) GEOMETRIC model to est. probab. of getting first success after certain # of
INDEPENDENT trials
b) BINOMIAL model to est. probab. of getting certain #successes in finite # of
INDEPENDENT trials
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
CHAPTER 18
SAMPLING DISTRIBUTION MODELS
WHERE ARE WE GOING?
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 will find out how much proportions from random samples will vary
 allows us to start generalizing from retrieved samples to popn
MAIN TXT
(example)
 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)
vary
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troops being withdrawn early from war

= 0.52
 ex. Strategic Counsel poll randomly selected same amt of Canadians and found
64% in favour

= 0.64
 both of these were properly selected random samples, but their prop's are strikingly
diff.
[2]
 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
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