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Week 1 Sept 1 - WEEK 1 Sept 1 Go over Syllabus Go over...

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1 WEEK 1 Sept 1 Go over Syllabus . Go over Tentative Schedule . Expected Coverage for Today . Ideas in Chapter 2, Sections 2-1 through 2-4. Types of probability : objective and subjective Probability models are used to mathematically model situations where outcomes are uncertain. Models can be useful although they cannot be proved to be correct. Example 1. A Coin Toss. I flip an ordinary coin, say, a U.S. quarter and let it land on a flat surface. Consider a model that ignores the possibility that it comes to rest on its edge. Then there are two possible outcomes for the upper face: Heads (H) and Tails (T). When we say the coin is fair , we imply that the two outcomes are equally likely. A mathematical expression for this is P(H) = P(T) = ½. The sample space S in the model is the collection of possible outcomes {H, T}. Here is a figure to display this probability model. ½ ½ . H .T S We might even use the simpler figure without the probabilities shown and simply state that the two outcomes are equally likely. . H .T S
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2 Example 2. Figure showing sample space with 11 outcomes. If the model specifies them as equally likely, then we know each has probability 1/11. The names of outcomes not shown in figure below; they are simply depicted by dots. . . . . . . . . . . . S Example 3. Model for independent tosses of three fair coins (say a nickel, a dime and a quarter). In the table below, the first letter denotes the outcome of the nickel, the second letter denotes the outcome of the dime, and the third letter denotes the outcome of the quarter.
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