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lecture14_2slides

# lecture14_2slides - Statistics 528 Lecture 14 Probability...

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Statistics 528 - Lecture 14 1 Statistics 528 - Lecture 14 Prof. Kate Calder 1 Probability Statistical Inference Question: How often would this method give the correct answer if I used it many times? Answer: Use laws of probability. Statistics 528 - Lecture 14 Prof. Kate Calder 2 Example: Tossing a coin If the coin is fair (chance of heads = chance of tails) then 1 toss - you don’t know whether you will get heads or tails Many tosses - the proportion of tosses where you get heads is close to 50% (IPS Probability Applet) => The outcome is predictable, but only in the long run .

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Statistics 528 - Lecture 14 2 Statistics 528 - Lecture 14 Prof. Kate Calder 3 Random: We call a phenomena random if individual outcomes are uncertain but there is a predictable pattern of outcomes in the long run. Note: Random Haphazard Probability: The probability of any outcome of a random phenomena is the proportion of times the outcome would occur in a large number of repetitions. (probability = long-term relative frequency) Statistics 528 - Lecture 14 Prof. Kate Calder 4 Probability Models Now let us try to model a random phenomenon. For example, consider tossing a fair coin. We don’t know the outcome in advance, but we can say the following: Possible outcomes: Heads, Tails Probability of each outcome: 0.5, 0.5
Statistics 528 - Lecture 14 3 Statistics 528 - Lecture 14 Prof. Kate Calder 5 A probability model consists of 1. sample space ( S ) – the set of all possible outcomes 2. probability for each outcome

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