Section4.1&amp;4.2posted

Section4.1&amp;4.2posted - STOR155,Section2...

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STOR 155, Section 2 Tuesday, March 2, 2010 Section 4.1 Section 4.2 through p. 250

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Chapter 4  Probability: the study of  randomness 4.1  Randomness 4.2  Probability models 4.3  Random variables 4.4  Means and variances of random  variables 4.5  General probability rules (not covered)
4.1 Randomness The language of probability Thinking about randomness The uses of probability

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The language of probability In statistics,  random  means more than just  unpredictable  or  haphazard. random phenomenon   is a situation in which  the outcome is uncertain, but  there would be a definite distribution of outcomes  if the  situation were repeated many times under identical  conditions . Examples toss a coin, note whether it comes up H or T take a SRS from a population, ask opinions on health insurance  reform bill deal two cards, then 5 more and note whether any of the 5  match one of the two Carolina-Miami basketball game? In each case, what would we expect for the distribution of  outcomes after many repetitions?
Language of probability:  Example 1 Phenomenon:  Deal 2 cards at random  from a shuffled deck.  Suppose they’re  different (not a pair).  Then deal 5 more  cards. Outcome of interest:  At least one of the 5  matches one of the 2. Empirical   estimation of the probability: In 100,000 simulated repetitions, the outcome  occurred on 48,722 repetitions.  So we  estimate the probability to be 48722/100000 =  0.48722.

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Language of probability:  Example 1 One  empirical  estimate of probability is  .48722 . Theoretical  approach:   Given that the first 2 cards are not a pair, 50 cards are  left; 6 of them match one of the 2, and 44 do not. Assume the deck is thoroughly shuffled so that every  remaining card has an equal chance of being dealt at  any time.  Then the probability of  no match   with five  new cards is     (44/50)×(43/49)×(42/48)×(41/47)×(40/46) =  0.5125677. So the probability of  at least one match  is  .5125677 =  .4874323 .
Thinking about randomness: two points to remember The repetitions we refer to must be a long series  of  independent trials   under  identical  conditions .  That is: the outcome of one trial must have no influence on  the outcome of any other trial, and the conditions of the repetition must be identical from  trial to trial. Probability is expected

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This note was uploaded on 06/12/2010 for the course STOR 155 taught by Professor Andrewb.nobel during the Spring '08 term at UNC.

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Section4.1&amp;4.2posted - STOR155,Section2...

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