notes509fall11sec31

notes509fall11sec31 - STAT 509 - Section 3.1: Probability...

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STAT 509 --- Section 3.1: Probability Basic Definitions Sample Space (of an experiment): The collection of all the possible outcomes (or sample points). Example 1. Record plant location (either 1, 2, 3) of next maintenance call for spinning machine repair: Sample space = Example 2. Toss 2 fair coins: Sample space = Example 3. An engineering design firm is up for a Nissan contract and a Ford contract: Sample space = The probability of a sample point is a number between 0 and 1 that measures the likelihood that this outcome will occur when the experiment is performed. Often we take this to mean the proportion of times the outcome would occur if we repeated the experiment many times. Note: (1) All sample point probabilities must be between 0 and 1. (2) The probabilities of all the points in the sample space must sum to 1.
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Plant 1 has 22 machines, plant 2 has 60 machines, plant 3 has 18 machines. Probability of next repair being from plant 3, denoted: P(3) = Assumption? An event is an outcome or collection of outcomes. We typically determine the probability of an event by adding the probabilities of the distinct outcomes that make up the event. Example 1: Event A = ‘next repair from odd-numbered plant’ P(A) = Example 3: Event B = ‘get at least one contract’ P(B) = Unions and Intersections Compound events are composed of two or more “simple events,” for example: The union of events A and B is the event that either A or B (or both) occurs. Denoted A
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notes509fall11sec31 - STAT 509 - Section 3.1: Probability...

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