203ch11+12_slides.pptx - STAT 203 Chapters 11 12...

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STAT 203 Chapters 11 & 12 Probability Consider throwing a thumbtack. The outcome can be a ‘point-up’ or ‘point-down’, but we cannot predict with certainty which outcome will occur before throwing the thumbtack. This is a random experiment. What is the chance or probability that the thumbtack lands with ‘point- up’? Let’s throw a thumbtack for a few times and look at the outcomes. Toss # Outcome (D-‘point-down’, U-‘point-up’) 1 2 3 4 5 D D U D U Based on the first five attempts or t rials , we have 40% ‘point-up’ and 60% ‘point-down’. Can we conclude the chance of landing with ‘point-up’ is 40%? Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 1
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STAT 203 Suppose for each additional toss, we compute the relative frequency of ‘point-up’ (i.e., the % of landing with ‘point-up’) from all the available tosses. Total # tosses #D’s #U’s relative freq. of U 1 1 0 0% (0/1) 2 2 0 0% (0/2) 3 2 1 33% (1/3) 4 3 1 25% (1/4) 5 3 2 40% (2/5) If we continue to throw the thumbtack and keep track of the relative frequency of ‘point-up’, we will see that the relative frequency eventually stabilizes at a single value. Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 2
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STAT 203 We can see it in the plot of the relative frequency against the number of tosses. The relative frequency of ‘point-up’ stays relatively constant at around 20% (say) for a large number of tosses. This long run relative frequency gives the probability of tossing a ‘point-up’, which is 20%. Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 3
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STAT 203 Probability concepts A sample space S is the set of of all possible outcomes of a random experiment. e.g., For tossing a coin, the sample space is the set { Head, Tail } . For rolling a die, the sample space is the set { 1,2,3,4,5,6 } . An event is an outcome or some outcomes from a random experiment. We denote an event by an uppercase letter, e.g., A, B, C. e.g., Tossing a head is an event. Tossing a tail is another event. Tossing two heads in two tosses is also an event. Eugenia Yu, UBC Department of Statistics. Not to be copied, used, or revised without explicit written permission from the copyright owner. 4
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STAT 203 The notation P ( A ) denotes the probability that an event A will occur.
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  • Winter '18
  • EugeniaHoiYinYu
  • Probability, Probability theory, Probability space, Eugenia Yu, UBC Department of Statistics

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