De…nitions and other formulas  Sections 3.1 to 3.3
De…nition 1 A
random variable
is any rule which associates a number with each outcome in a
sample space.
De…nition 2
Any random variable whose only possible values are 0 and 1 is called a
Bernoulli
random variable
.
De…nition 3
A set is
discrete
either if it consists of a …nite number of elements or if its elements
can be listed in
sequence so that there is a …rst element, a second element, a third element, and so on, in the list.
De…nition 4
A random variable is said to be
discrete
if its set of possible values is a discrete set.
De…nition 5
The
probability distribution
or
probability mass function
(pmf) of a discrete
random variable is de…ned for every number
x
by
p
(
x
) =
P
(
X
=
x
) =
P
(
all
s
2
S
:
X
(
s
) =
x
)
.
De…nition 6
Suppose
p
(
x
)
depends on a quantity that can be assigned any one of a number of
possible values, with each di¤erent value determining a di¤erent probability distribution. Such
a quantity is called a
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 Fall '10
 Staff
 Probability theory

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