Stats: Chapter 10

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Author:
muk.muk
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42312
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Stats: Chapter 10
Updated:
2010-10-14 23:53:38
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statistics midterm
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Chapter 10 definitions
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  1. Chance/Random Phenomenon
    Has unpredictable behavior in the short run but has a regular and predictable pattern in the long run
  2. Probability
    • Studies the likelihood of occurrence of random events in order to predict the behavior of defined systems.
    • Only describes what happens in the long run
  3. Sample Space S
    • The set of all possible outcomes in a random phenomenon
    • The set of all outcomes are caleld events
    • 1 event is the subset of the sample space
  4. Probability Model
    Description of a random phenomenon consisting of a sample space S and a way of assigning probabilities to events
  5. Probability Rules
    • A number between 0 - 1 is a probability number
    • All possible outcomes together must have a probability of one
    • If two events have no outcomes in common the probability that one or the other occurs is the sum of their individual probabilities
    • The probability that an event occurs is 1 minus the probability that the event does not occur

    e.g. If event 1 occurs 50% of the time and a diff event occurs 25% of the time, then the chance of one or the other occuring is 75%
  6. Probability numbers. What does 0, 0.5, and 1 mean?
    • 0 = never occurs
    • 1 = always occurs
    • 0.5 occurs half the trials
  7. 0 < P(A) <= 1
    A number between 0 - 1 is a probability number
  8. P(S) = 1
    The sample space S always equals 1
  9. P(A or B) = P(A) + P(B)
    • If A and B are disjoints if they have no outcomes in common
    • The chance of one of them occuring is the sum of the two probabilities
  10. P(A does not occur) = 1 - P(A)
    The probability of an event that does not occur is 1 - the probability that the event does occur
  11. Discrete Probability Model
    • A model with a finite sample (has limits)
    • The prob of any event is the sum of the probabilities of all the values that make up the event
    • This model assigns each of these values a probability between 0 and 1 such that the sum of all the probabilities is 1
  12. Continuous Probability Model
    • Assigns the probabilities as areas under a density curve
    • The probability of any event is the area under the curve above the values that make up the event
  13. Random Variable
    A variable whose value is a numerical outcome of a random phenomenon
  14. Probability Distribution
    The random variable X tells us what the possible values of X are and how probabilities are assigned to those values

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