ENMA 420-520 Lecture 2 Slides_1

ENMA 420-520 Lecture 2 Slides_1 - Statistical Concepts for...

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Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #2 Probability 11
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10/17/09 Basic Definitions Experiment: the process of obtaining an observation or taking a measurement. Simple event: the basic outcome of an experiment; cannot be decomposed into simpler outcomes. Sample space: the collection of all possible simple events. 22
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10/17/09 Probability The probability of a simple event is the number that measures the likelihood that the event will occur when the experiment is performed. The probability can be approximated by the proportion of times that the simple event is observed when the experiment is repeated a very large number of times. For a simple event 33
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10/17/09 Probability of an Event Event: a specific collection of simple events. Probability of an event A = the sum of the probabilities of the simple events in event A. 44
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10/17/09 Calculating a Probability 1. Define the experiment: the process used to make an observation and the type of observation that will be recorded. 2. Define and list the simple events. 3. Assign probabilities to the simple events. 4. Determine the collection of simple 55
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10/17/09 Exercise 3.2 a. The sample space will include the following simple events: Single, shore parallel Planar Other b. The probabilities for the simple events are shown in the table below: Simple Event Probabilities Single, shore parallel 2/6 66
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10/17/09 Exercise 3.4 a. 27 of the 83 industrial accidents were caused by faulty engineering and design. We say that the probability of faulty engineering and design causing an industrial accident is 27/83 = 0.3253. About one-third of all industrial accidents are caused by faulty engineering and design. b. 59 of the 83 industrial accidents 77
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10/17/09 Compound Events The union of two events A and B is the event that occurs if either (or both) A or B occur on a single performance of the experiment: A & B = A or B The intersection of two events A and B is the event that occurs if both A or B occur on a single performance of the experiment: 88
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10/17/09 Side Note Exclusive-OR (XOR) is the operator for A or B but NOT both: A & B = A or B but not both 99
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10/17/09 Complementary Events The complement A’ of the event A is the event that A does not occur. This is the event consisting of all simple events that are not in event A. The sum the probabilities of complementary events is 1: P(A) + P(A’) = 1 1010
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10/17/09 Exercise 3.14 A summary for the MTBE data set is 1111 MTBE Level Aquifer Below level Detectable level Total Bedrock 138 63 201 Unconsolidate d 15 7 22 Total 153 70 223
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10/17/09 Exercise 3.14 (Cont’d) 1212 P(Detectable Level) P(Bedrock ) P(Bedrock and Detectable Level) = P (B & D) P(Bedrock or Detectable Level) = P (B & D) P (B& &D)
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10/17/09 Exercise 3.18 a. The simple events in A» B are the numbers that are odd or black or both and are: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35} A – B consists of 28 of the 38 equally likely simple events.
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ENMA 420-520 Lecture 2 Slides_1 - Statistical Concepts for...

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