# Stats: Chapter 10

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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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 Author: muk.muk ID: 42312 Filename: Stats: Chapter 10 Updated: 2010-10-15 03:53:38 Tags: statistics midterm Folders: Description: Chapter 10 definitions Show Answers:

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