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Chapter 14

STAB22- Chapter 14, Butler, Summer 2012, Textbook Notes


Department
Statistics
Course Code
STAB22H3
Professor
Ken Butler
Chapter
14

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CHAPTER 14: FROM RANDOMNESS TO PROBABILITY
WHERE ARE WE GOING?
- random in the short-term, predictable in long-term
(ex) Flipping a coin
- cannot predict oucome of one flip b/c its random
- but if its
fair
coin, then can predict
proportion
of heads likely to see in long-
term
- focus of this chapter and subsequent: long-term predictability of randomness
Ways of assessing randomness
- empirically
- ex. weather forecaster says that there is 40% chance of rain, and they did this
by looking at past maps that're similar to today's, and finding % of those that were
rainy days
- theoretically
- ex. odds of winning 6/49 jackpot are 1 in 14 million
- subjectively
- ex. Susie arrives at her likelihood getting an A based on how she views course
material, her study habits and her optimistic views
p377
EMPIRICAL PROBABILITY
[1]

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(ex) of RANDOM PHENOMENON
- whether light is red, green, or yellow as
you
reach intesection
- pattern of own driving is random
- its not signal lighting, b/c that is lit a certain colour precisely at, and for
certain time interval's
[2]
- as we see more and more outcomes, overall % of times that light is approaching a
certain val.
- as new data val's are recorded, each new outcome becomes smaller and smaller prop.
of overall experience
- the val. is approaching is the likelihood
(ex)
- plot of % green light against days
- graph begins at 100%, b/c the first time, we ran into light being green, so 1/1 =
100%

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

- but then next day, it became red => accumulated% of light being green now
50% 1/2 are green
... so on and so forth
- if we continue approaching this light at random, then can find that
%Green will approach some fixed val.
(ex) as you incr. number of days, % of light being green is about 35% of the time
- we are only interested in colour of light at time when we drive to that
intersection, not the traffic light colour the entire day
- per day, only looking at that instance when we came to that
intersection, and recorde dwhat colour light it was
- despite randomnes deriving from uncertainty as to time for us to get to intersection,
we can think of light itself as showing colour at random
- based on what time we come at
TERMINOLOGY
p378
[1]
- TRIAL - each occasion upon which a random phenomenon is observed
- OUTCOME - val. of random phenomenon at each trial
=> phenomenon consists of trials
- each trial corresponds to one outcome
- outcomes combine to make events
[2]
(ex) traffic light
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