Starnes, UPDATED The Practice of Statistics, 6e, Chapter 5

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19 Terms

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random process
Generates outcomes that are determined purely by chance.
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probability
THIS of any outcome of a random process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long A trial is one repetition of a random series of trials.
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law of large numbers
Says that if we observe more and more trials of any random process, the proportion of times that a specific outcome occurs approaches its probability.
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simulation
Imitates a random process in such a way that simulated outcomes are consistent with real-world outcomes.
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probability model
A description of some random process that consists of two parts: a list of all possible outcomes and the probability for each outcome.
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sample space
The list of all possible outcomes.
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event
Any collection of outcomes from some random process.
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Complement rule, Complement
THIS says that 𝑃(Aᶜ)=1−𝑃(A), where Aᶜ is the "THIS" of event A; that is, the event that A does not occur.
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mutually exclusive (disjoint)
Two events A and B are "THIS" if they have no outcomes in common and so can never occur together—that is, if 𝑃(A and B) = 0.
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Addition rule for mutually exclusive events
For A and B says that 𝑃(A or B) = 𝑃(A) + 𝑃(B)
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general addition rule
If A and B are any two events resulting from some random process, the "THIS" says that 𝑃(A or B) = 𝑃(A) + 𝑃(B) − 𝑃(A and B)
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Venn diagram
Consists of one or more circles surrounded by a rectangle. Each circle represents an event. The region inside the rectangle represents the sample space of the random process.
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intersection
The event “A and B” is called the "THIS" of events A and B. It consists of all outcomes that are common to both events, and is denoted A∩B.
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union
The event “A or B” is called the "THIS" of events A and B. It consists of all outcomes that are in event A or event B, or both, and is denoted A∪B.
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conditional probability
The probability that one event happens given that another event is known to have happened. The "THIS" that event A happens given that event B has happened is denoted by 𝑃(A|B).
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independent events
A and B are THIS if knowing whether or not one event has occurred does not change the probability that the other event will happen. In other words, events A and B are THIS if 𝑃(A|B) = 𝑃(A|Bᶜ) = 𝑃(A). Alternatively, events A and B are THIS if 𝑃(B|A) = 𝑃(B|Aᶜ) = 𝑃(B)
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general multiplication rule
For any random process, the probability that events A and B both occur can be found using the "THIS": 𝑃(A and B)= 𝑃(A∩B) = 𝑃(A) * 𝑃(B|A)
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tree diagram
Shows the sample space of a random process involving multiple stages. The probability of each outcome is shown on the corresponding branch of the tree. All probabilities after the first stage are conditional probabilities.
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Multiplication rule for independent events
If A and B are independent events, the probability that A and B both occur is 𝑃(A and B) = 𝑃(A∩B) = 𝑃(A) * 𝑃(B)