PSLS.PPT.Ch09

PSLS.PPT.Ch09 - Introducingprobability PSLS chapter 9 2009...

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    Introducing probability PSLS chapter 9 © 2009 W. H. Freeman and Company
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Objectives (PSLS chapter 9) Introducing probability Randomness and probability Probability models Discrete vs continuous sample spaces Probability rules Random variables Meaning of a probability Risk and odds
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A phenomenon is random if individual outcomes are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions. Randomness and probability The probability of any outcome of a random phenomenon can be defined as the proportion of times the outcome would occur in a very long series of repetitions.
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Ex: Coin toss First series of tosses Second series Probability of heads is 0.5 = proportion of times you get heads in many repeated trials
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Probability models mathematically describe the outcome of random processes. They consist of two parts: 1) S = Sample Space: This is a set, or list, of all possible outcomes of a random process. An event is a subset of the sample space. 2) A probability for each possible event in the sample space S. Probability models Example: Probability Model for a Coin Toss S = {Head, Tail} Probability of heads = 0.5 Probability of tails = 0.5
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Important: It's the question that determines the sample space. Sample space A. A couple wants 3 children. What are the possible sequences of boys (B) and girls (G)? B B B - BBB G G G - BBG B - BGB G - BGG S = { BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG } Note: 8 elements, 2 3 B. A couple wants 3 children. What is the number of girls they could have? S = { 0, 1, 2, 3 } C. A researcher designs a new maze for lab rats. What are the possible outcomes for the time to finish the maze (in minutes)? S = ] 0, ∞] = (all numbers > 0)
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Discrete variables contrast with continuous variables that can take on any one of an infinite number of possible values over an interval. Blood types For a random person: S = {O+, O-, A+, A-, B+, B-, AB+, AB-} and the probability of each event reflects the population frequencies Discrete vs. continuous sample spaces Finite sample spaces deal with discrete variables that can take on only certain values (e.g. a whole number or a descriptor).
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This note was uploaded on 10/07/2011 for the course BSTT 400 taught by Professor Sallyfreels during the Fall '11 term at Ill. Chicago.

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PSLS.PPT.Ch09 - Introducingprobability PSLS chapter 9 2009...

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