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

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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%
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- 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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Document Summary

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. 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. Ex. odds of winning 6/49 jackpot are 1 in 14 million. Susie arrives at her likelihood getting an a based on how she views course material, her study habits and her optimistic views p377. Whether light is red, green, or yellow as you reach intesection. Pattern of own driving is random certain time interval"s. Its not signal lighting, b/c that is lit a certain colour precisely at, and for.

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