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Ken Butler (10)

Chapter 14

Department

StatisticsCourse Code

STAB22H3Professor

Ken ButlerChapter

14This

**preview**shows pages 1-3. to view the full**26 pages of the document.**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]

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

(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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