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Ken Butler (10)

Chapter 17

Department

StatisticsCourse Code

STAB22H3Professor

Ken ButlerChapter

17This

**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

[1]

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

[2]

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.

[3]

Crosby scenario is example of BERNOULLI TRIALS

BERNOULLI TRIALS, if

[1]- 2 possible outcomes

>- p = success, q = failure

- note that it does not req. 0.50 = p, 0.50 = q

[2]- P(success) constant

[3]- trials indep.

- other ex's

>- tossing a coin

[1] either get heads (Success), or get tails (failure)

[2] P(success) = 0.5

[3] 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

[1] either get shot (success) or miss (failure)

[2] P(success) = 0.70 (ie. this player has 70% chance of getting in)

[3] 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

[4]

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.

[5]

- 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

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