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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 π(AαΆ)=1βπ(A), where AαΆ 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 togetherβthat is, if π(A and B) = 0.

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Addition rule for mutually exclusive events

For A and B says that π(A or B) = π(A) + π(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 π(A or B) = π(A) + π(B) β π(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 βA and Bβ is called the "THIS" of events A and B. It consists of all outcomes that are common to both events, and is denoted Aβ©B.

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union

The event βA or Bβ 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 AβͺB.

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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 π(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 π(A|B) = π(A|BαΆ) = π(A). Alternatively, events A and B are THIS if π(B|A) = π(B|AαΆ) = π(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": π(A and B)= π(Aβ©B) = π(A) * π(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 π(A and B) = π(Aβ©B) = π(A) * π(B)

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