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STAB22-C18.docx

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Department
Statistics
Course
STAB22H3
Professor
Ken Butler
Semester
Summer

Description
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. 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? - 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 Angus reid poll randomly selected 1k Canadians and found 52% in favour of troops being withdrawn early from war - = 0.52 - ex.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 [1] (ex) Strategic Counsel poll - imagine results from all random samples of size 1,000 that the poll-administrators did not take - what would histogram for sample prop's retrieved from each one sample collectively look like? [2] (ex) Strategic Counsel poll - the centre of this histogram is the true proportion in the popn - denoted as p ---- NOTATION ALERT - p = true (gen. unk) prop. of successes in popn - = sample prop - estimate of p derived from data - q-hat = sample prop. of failures - q = true (gen. unk) prop. of failures in popn --- - suppose that p = 0.60 - 60% of ALL Canadian adults supported early withdrawl. [3] Shape of histogram? (ex) Strategic Counsel poll
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