Probability Theory

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Probability theory
Probability: A numerical measure of the chance that an event will occur. Experiment: A process that generates well defined outcomes.
Sample space: The set of all experimental outcomes.
Sample point: An element of the sample space. A sample point represents an experimental outcome. Tree diagram: A graphical representation that helps in visualizing a multiple step experiment. Classical method: A method of assigning probabilities that is appropriate when all the experimental outcomes are equally likely. Relative frequency method: A method of assigning probabilities that is appropriate when data are available to estimate the proportion of the time the experimental outcome will occur if the experiment is repeated large number of times. Subjective method: A method of assigning probabilities on judgment. Event: A collection of sample points.

Complement of A : The event consisting of all sample points that are not in A. Venn diagram: A graphical representation for showing symbolically the sample space and operations involving events in which the sample space is represented by a rectangle and events are represented as circles within the sample space. Union of A and B : The event consisting of all sample points belonging to A or B or both. Intersection of A and B : The event containing the sample points belonging to both A and B. Conditional probabilities: the probability of an event given that another event already occurred. Joint probability: The probability of two events both is occurring that is the probability of the intersection of two events. Marginal probabilities: The values in the margins of a joint probability table that provides the probabilities of each event separately. Independent events: Two events A and B where the events have no influence on each other. Priory probabilities: Initial estimates of the probabilities of events. Posterior probabilities: revised probabilities of events based on additional information. Bayes’ theorem: A...
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