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Chapter 17

# STAB22- Chapter 17, Butler, Summer 2012, Textbook Notes

Department
Statistics
Course Code
STAB22H3
Professor
Ken Butler
Chapter
17

This preview shows pages 1-3. to view the full 24 pages of the document. CHAPTER 17 - PROBABILITY MODELS
WHERE ARE WE GOING?
- learning about probability models in this chapter
MAIN TEXT
Recall qn: "Suppose a cereal manufacturer puts pic's of famous atletes on cards in
boxes of cereals, for hope of incr'ing sales. Manufacturer announces that
- 20% Crosby
- 30% Beckham
- 50% Williams
p446
SEARCHING FOR CROSBY

QN: How many cereal boxes to open before we get Sidney Crosby pic

assumption:
- pic's are randomly distributed
- probabilities are correct
(ex)
- 20% of cards are Crosby => probability of finding Crosby is 0.20
- in this case, trial = opening each box, and
>1- only 2 possible outcomes exist (failure or success)
(ex)

Only pages 1-3 are available for preview. Some parts have been intentionally blurred. - you either get Crosby's pic (success), or you do not (failure)
>2- probability of success (p) is same ON EVERY TRIAL
(ex)
p = 0.20
>3- trials are independent
(ex)
finding Crosby in first box doesn't change what will occur when you reach for next box.

Crosby scenario is example of BERNOULLI TRIALS
BERNOULLI TRIALS, if
- 2 possible outcomes
>- p = success, q = failure
- note that it does not req. 0.50 = p, 0.50 = q
- P(success) constant
- trials indep.
- other ex's
>- tossing a coin
 either get heads (Success), or get tails (failure)
 P(success) = 0.5
 getting heads on one trial does not affect outcome you get on next trial

Only pages 1-3 are available for preview. Some parts have been intentionally blurred. - shooting free throws in basketball game
 either get shot (success) or miss (failure)
 P(success) = 0.70 (ie. this player has 70% chance of getting in)
 what he gets on one trial is assumed to not affect his outcome on the next trial
WHAT CAN WE DO WITH BERNOULLI TRIALS?
- B.trials are used to construct wide range of various, but useful probability models

Crosby (ex)
QN: how many boxes do we have to open to find Crosby?
- Let random variable Y = #boxes
- What is probability of finding his picture in FIRST box of cereal?
P(Y = 1) = 0.20
- Y = 1 is telling us that #boxes [opened] is 1.

- What is probability of finding his picture in SECOND box of cereal?
P(failure) = q = 0.80
P(success) = p = 0.20
So, P(Y = 2) = (0.20)(0.80) = 0.160
- trials are independent, so we can multiply like that