2.2. SAMPLE SPACES
-An
experiment
is any process of observation or measurement.
-The result one obtains from an experiment are called the
outcome
of the experiment.
-The set of all possible
outcomes
of an experiment is called the
sample space (S)
.
-Each outcome in a
sample space
is called an
element
of the sample space (or simply a
sample point
)
-If a
sample space
has a finite number of
elements
, we list the elements using the
following notation:
S = {H,T}
S = {1,2,3,4,5,6}
-If a sample space has a large or infinite number of elements, we describe the elements.
For example, “S is the set of all x such that x is an automobile with a CB radio.”
S = {x| x is an automobile with a CB radio}
For example, “S is the set of odd positive integers”
S = {2k+1| k=0,1,2…}
-If a sample space can be matched one-to-one with whole numbers, it is said to be
countable
. A sample space with an infinite number of elements
can
be countable:
S = {H, TH, TTH, TTTH, TTTTH,…}
-If a sample space contains a finite number of elements
or
an infinite
though
countable
number of elements, it is said to be discrete.
-Some sample spaces are not
discrete
, meaning they do not contain a finite number of
elements
or
an infinite number of elements which are countable. (For example,
measuring the time of a chemical reaction)
If a sample space consists of a continuum, such as all the points of a line segment or all
the points in a plane, it is said to be
continuous
.
2.3. EVENTS
-In many problems we are interested in results that are not given directly by a specific
element of a sample space.
Rather, the results will be a
collection
of elements within the
sample space (a
subset
of the sample space).
“By definition, an
event
is a subset of a sample space.”
-In many problems of probability we are interested in events that are actually
combinations of two or more events, formed by taking
unions, intersections,
and
complements.
-If