Midterm Concepts Flashcards
The set of all possible outcomes of a statistical experiment is called the
sample
space (S)
Each outcome in a sample space is called an
element
In some
experiments, it is helpful to list the elements of the sample space systematically by
means of a
tree diagram
Sample spaces with a large or infinite number of sample points are best described by a
statement or rule method
An _____ is a subset of a sample space.
event
The ______ of an event A with respect to S is the subset of all elements
of S that are not in A.
complement
The ______ of two events A and B, denoted by the symbol A ∩ B, is the
event containing all elements that are common to A and B.
intersection
Two events A and B are _______, or disjoint, if A ∩ B = φ, that
is, if A and B have no elements in common.
mutually exclusive
The ______ of the two events A and B, denoted by the symbol A∪B, is the event containing all the elements that belong to A or B or both.
union
The relationship between events and the corresponding sample space can be
illustrated graphically by means of
Venn diagrams
The fundamental principle of counting, often referred
to as the ______
multiplication rule
A ______ is an arrangement of all or part of a set of objects.
permutation
Permutations that occur by arranging objects in a circle are called ________
circular
permutations
Often we are concerned with the number of ways of partitioning a set of n
objects into r subsets called
cells
In many problems, we are interested in the number of ways of selecting r objects
from n without regard to order. These selections are called _______
combinations
The likelihood of
the occurrence of an event resulting from such a statistical experiment is evaluated
by means of a set of real numbers, called weights or ________
probabilities
The _______ of an event A is the sum of the weights of all sample points in
A.
probability
The probability of an event B occurring when it is known that some event A
has occurred is called a ______ and is denoted by P(B|A).
conditional probability
A generalization of the foregoing illustration to the case where the sample space
is partitioned into k subsets is covered by the following theorem, sometimes called
the _______
theorem of total probability or the rule of elimination
A _______ is a function that associates a real number with each element
in the sample space
random variable
The random variable for which 0 and 1 are chosen
to describe the two possible values is called a _______
Bernoulli random variable
If a sample space contains a finite number of possibilities or an unending sequence
with as many elements as there are whole numbers, it is called a
discrete sample space
If a sample space contains an infinite number of possibilities equal to the number
of points on a line segment, it is called a _______
continuous sample space
In dealing with
continuous variables, f(x) is usually called the the ______, of X.
density function
We shall refer
to this average value as the ____ of the random variable X
mean
The positive square root of the variance, σ, is called the ______ of
X.
standard deviation
The probability distribution of this discrete random variable is called
the
binomial distribution
The ______ does not
require independence and is based on sampling done without replacement.
hypergeometric distribution
The number X of trials required to produce k successes in a negative binomial
experiment is called a negative binomial random variable, and its probability
distribution is called the
negative binomial distribution
Experiments yielding numerical values of a random variable X, the number of
outcomes occurring during a given time interval or in a specified region, are called
_____
Poisson experiments
