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| a phenomenon is random if we know what outcomes could happen, but not which particular values will happen |
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| a single attempt or realization of a random phenomenon |
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| the outcome of a trial is the value measured, observed, or reported for an individual instance of that trial |
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| a collection of outcomes; usually we identify events so that we can attach probabilities to them; denoted with bold capital letters |
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| the collection of all possible outcome values; sample space has a probability of 1 |
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| LLN states that the long-run relative frequency of repeated independent events gets closer and closer to the true relative frequency as the number of trials increases |
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| Independence (informally) |
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| Two events are independent if learning that one event occurs does not change the probability that the other event occurs |
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| a number between 0 and 1 that reports the likelihood of that event's occurrence; we write P(A) for the probability of the event A |
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| when the probability comes from the long-run relative frequency of the event's occurrence |
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| when the probability comes from a model (such as equally likely outcomes) |
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| when the probability is subjective and represents your personal degree of belief |
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| The Probability Assignment Rule |
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| the probability of the entire sample space must be 1 |
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| the probability of an event occurring is 1 minus the probability that it doesn't occur |
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| Disjoint (mutually exclusive) |
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| two events are disjoint if they share no outcomes in common; if A and B are disjoint, knowing that A occurs tells us that B cannot occur; also called mutually exclusive |
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Definition
| If A and B are disjoint events, then the probability of A or B is P (A U B) = P(A) + P(B) |
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| Legitimate probability assignment |
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Definition
| an assignment of probabilities to outcomes is legitimate if each probability is between 0 and 1 (inclusive) and the sum of the probabilities is 1 |
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Definition
| If A and B are independent events, then the probability of A and B is P(A)*P(B) |
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| we often require events to be independent (so you should think about whether this assumption is reasonable) |
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