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Definition
- outcome is uncertain
- short-run proportion of occurences very random
- Long run more predictable
- Probability quantifies long-run randomness
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- as number of trials increase, proportion of occurrences of any given outcome approaches a particular number
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- outcome of any one trial is not affected by the outcome of nay other trial
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Definition
- Calculate theoretical probabilities based on assupmtions about the random pehnomena
- Observe many trials of random phenomenon and use sample proportion of the number of occurences as probability
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Definition
- Long run proportion of times that the outcome occurs in a very large number of trials
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- When long-run trials not feasible
- probability of outcome is your degree of belief the outcome will occur
- Bayesian statistics uses subjective probability.
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Definition
- For random phenomenon:
- sample space is the set of all possible outcomes
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- subset of sample space
- even corresponds to particular outcome or a group of possible outcomes
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Term
| Probabilities for a sample space |
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Definition
- Each outcome in sample space has a probability
- The probability of each individual outcome is between 0 and 1
- total of all individual probabilities equals 1
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Definition
- Probability of an event A = P(A)
- P(A) = (number of outcomes in event A)/(Number of outcomes in the sample space)
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Definition
- Complement of event A consists of all outcomes in sample space that are not in A
- Probabilities of A and of Ac (complement) sum to 1
- P(Ac) = 1- P(A)
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Definition
- events do not have any common outcomes
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Definition
- Outcomes that are common in both events
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Definition
- Consists of outcomes that are in even A or B or in both A and B
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Term
| Probability of Union of 2 events |
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Definition
- Addition Rule
- For the union of 2 events
- P(A or B) = P(a) + P(B) - P(A and B)
- If the events are disjoint, P(A and B) = 0
- Thus: P(A or B) = P(A) + P(B)
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| Probability of Intersection of Two Events |
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- Multiplication Rule
- For the intersection of 2 independent Events A and B
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Term
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Definition
- For events A and B, Conditional probability of event A give that event B has occurred is
- P(A|B) = P(A and B)/P(B)
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| Pultiplication Rule for Finding P(A and B) |
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Definition
- P(A and B) = P(A|B) x P(B)
- P(A and B) = P(B|A) x P(A)
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Term
| Efinition of Independent Events using conditional probability |
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Definition
- 2 events A and B are independent if probability that one occurs is not affected by the other
- Independent if
- P(A|B) = P(A) or P(B|A)=P(A)
- P(A and B) = P(A) x P(B)
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Term
| Is a "Coincidence truly an unusual event? |
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Definition
- Law of very large numbers states that if something has a very large number of opportunities to happen, occasionally it will happen even if unusual
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Definition
- specifies possible outcomes for sample space and provides assumptions on which probability calculations for events composed of these outcomes are based
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| carrying out a Simulation |
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Definition
- Identify random phenomenon to be simulated
- Describe how to simulate observations
- Carry out simulation many times
- Summarize results and state the conclusion
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