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| the science of uncertainty |
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| an action whose outcome cannot be predicted with certainty |
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Term
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Definition
some specified result that may or may not occur when an experiment is performed
a collection of outcomes for the experiment, that is, any subset of the sample space. An event occurs if and only if the outcome of the experiment is a member of the event. |
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Definition
| each experimental unit is equally likely to be the one obtained |
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| frequentist interpretation of probability |
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Definition
| construes the probability of an event to be the proportion of times it occurs in a large number of repetitions of the experiment |
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| a mathematical description of the experiment based on certain primary aspects and assumptions |
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| an example of a probability model whose primary aspect and assumption are that all possible outcomes are equally likely to occur |
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| basic properties of probabilities |
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Definition
1. the probability of an event is always between 0 and 1, inclusive
2. the probability of an event that cannot occur is 0. (an event that cannot occur is called an impossible event)
3. the probability of an event that must occur is 1 (an event that must occur is called a certain event) |
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Definition
| the collection of all possible outcomes for an experiment |
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| one of the best ways to portray events and relationships among events visually. Sample space is depicted as a rectangle, and the various events are drawn as disks inside the rectange |
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| complement (denoted not E) |
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Definition
| consists of all outcomes not in E |
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| mutually exclusive events |
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Definition
| two or more events are mutually exclusive if no two of them have outcomes in common |
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Definition
| if E is an event, then P(E) represents the probability that event E occurs. It is read "the probability of E" |
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Definition
| for mutually exclusive events, the probability that one or another of the events occurs equals the sum of the individual probabilities |
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Definition
| the probability an event occurs equals 1 minus the probability the event does not occur |
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Definition
for events that are not mutually exclusive
If A and B are any two events, then
P(A or B) = P(A) + P(B) - P(A & B) |
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Definition
the probability that the event occurs under the assumption that another event occurs
The probability that event B occurs given that event A occurs
P(A & B) / P(A) |
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| general multiplication rule |
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Definition
for any two events, the probability that both occur equals the probability that a specified one occurs times the contitional probability of the other event, given the specified event
If A and B are any two events
P(A & B) = P(A) * the probability of B given A |
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Term
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Definition
| one event is independent of another event if knowing whether the latter event occurs does not affect the probability of the former event |
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| special multiplication rule |
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Definition
two events are independent if and only if the probability that both occur equals the product of their individual probabilities
If A and B are independent events then
P(A & B) = P(A) * P(B) |
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Term
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Definition
| events are said to be exhaustive if one or more of them must occur |
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| rule of total probability (stratified sampling theorum) |
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Definition
| Let A1, A2,...,Ak be mutually exclusive and exhaustive events. Then the probability of an event B can be obtained by multiplying the probability of each Aj by the contitional probability of B given Aj and then summing the products |
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| Basic Counting Rule (BCR) |
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Definition
| the total number of ways that several actions can occur equals the product of the individual number of ways for each action |
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Term
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Definition
| the factorial of a counting number is obtained by successively multiplying it by the next smaller counting number until reaching 1 |
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Definition
| a permutation of r objects from a collection of m objects is any ordered arrangement of r of the m objects |
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Term
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Definition
the number of possible permutations of r objects from a collection of m objects is given by the formula
m! / (m - r)! |
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| special permutations rule |
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Definition
| the number of possible permutations of m objects among themselves is m! |
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Term
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Definition
the number of possible combinations of r objects from a collection of m objects is given by the formula
m! / r!(m-r)! |
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Term
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Definition
| a combination of r objects from a collection of m objects is any unordered arrangement or r of the m objects--in other words, any subset of r objects from the collection of m objects (order matters in permutations, but not combinations) |
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