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10 Cards in this Set
- Front
- Back
event
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any collection (set) of outcomes of a random procedure (denoted with uppercase italicized letter, e.g. A)
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simple event
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consists of a single outcome
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sample space
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the set of all possible outcomes of random experiment (e.g. flip a coin, roll a die) (each element is an outcome)
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relative frequency (A)
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relative frequency (A) = # times a occurs/# of trials
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definition of probability
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Probability is the expected long-term relative frequency of an event (that is, the proportion of the time that we’d expect that particular event to occur in the long run).
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Approaches to get probability
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1) “classical” (theoretical)
When all outcomes in the sample space are equally likely P(A) = #(A) / #(S) (coin toss, roll die A = {3, 4, 5, 6}, B = {1, 3, 5}, C = {1, 2, 3}, and D = {2, 4}) 2) relative frequency (empirical) 3) subjective (personal) |
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Law of Large Numbers (LLN)
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As a procedure is repeated again and again, the relative frequency probability of an event tends to approach the actual probability
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Prob of event P(A)
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0 <= P(A) => 1
P = 0 = A impossible P = 1 = A certain |
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Independent events
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Two events A and B are independent if the occurrence of one does not affect the probability of the other's occurrence.
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Dependent events
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If A occures it increases the prob of B occurring
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