Chapter 4 Flashcards
Addition Law
A probability law used to compute the probability of the union of two events. It is P(A ∩ B) = P(A) + P(B) − P(A ∪ B). For mutually exclusive events, P(A ∩ B) = 0; in this case the addition law reduces to P(A ∪ B) = P(A) + P(B).
Basic requirements for assigning probabilities
Two requirements that restrict the manner in which probability assignments can be made: (1) for each experimental outcome E; we must have 0 < P(E;) < 1; (2) considering all experimental outcomes, we must have
P(El) + P(Ez) +
.+P(E,)卡1.0
Bayes’ Theorom
A method used to compute posterior probabilities.
Classical Method
A method of assigning probabilities that is appropriate when all the experimental outcomes are equally likely.
Combination
In an experiment we may be interested in determining the number of ways n objects may be selected from among N objects without regard to the order in which the n objects are selected. Each selection of n objects is called a combination and the total number of combinations of N objects taken n at a time is
Complement of A
The event consisting of all sample points that are not in A.
Conditional Probability
The probability of an event given that another event already occurred. The conditional probability of A given B is
P(A B) =
P(AMB)
P(B)
Event
A collection of sample points.
Experiment
A process that generates well-defined outcomes.
Independant Events
Two events A and B where P(A | B) = P(A) or P(B | A) = P(B); that is, the events have no influence on each other.
Intersection of A and B
The event containing the sample points belonging to both A and B. The intersection is denoted A ∩ B.
Joint Probability
The probability of two events both occurring; that is, the probability of the intersection of two events.
Marginal Probability
The values in the margins of a joint probability table that provide the probabilities of each event separately.
Multiple-Step Experiment
An experiment that can be described as a sequence of steps.
If a multiple-step experiment has k steps with n1 possible outcomes on the first step, n2 possible outcomes on the second step, and so on, the total number of experimental outcomes is given by (nI) (12)… (nk).
Multiplication Law
A probability law used to compute the probability of the intersection of two events. It is P(A ∩ B) = P(B)P(A | B) or P(A ∩ B) = P(A)P(B | A). For independent events it reduces to P(A ∩ B) = P(A)P(B).
Mutually Exclusive Events
Events that have no sample points in common; that is, A ∩ B is empty and P(A ∩ B) = 0.
Permutation
In an experiment we may be interested in determining the number of ways n objects may be selected from among N objects when the order in which the n objects are selected is important. Each ordering of n objects is called a permutation and the total number of permutations of N objects taken n at a time is for n = 0, 1, 2, …, N.
Posterior Probabilities
Revised probabilities of events based on additional information.
Prior Probabilities
Initial estimates of the probabilities of events.
Probability
A numerical measure of the likelihood that an event will occur.
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 a large number of times.
Sample Point
An element of the sample space. A sample point represents an experimental outcome.
Sample Space
The set of all experimental outcomes.
Subjective Method
A method of assigning probabilities on the basis of judgment.
Tree Diagram
A graphical representation that helps in visualizing a multiple-step experiment.
Union of A and B
The event containing all sample points belonging to A or B or both. The union is denoted A ∪ B.
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.
