Section 8.1 – Distributions of Random Variables
1
Section 8.1
Distributions of Random Variables
A rule that assigns a number to each outcome of an experiment is called a
random
variable.
Capital letters are often used to represent random variables.
For example, a random variable
X
can represent the sum of the face values of two six-
sided dice.
The random variable may take on any number in the set {2, 3, …, 12}.
We can construct the probability distribution associated with a random variable.
If
x
1
, x
2
, x
3
,…, x
n
are values assumed by the random variable
X
with associated
probabilities
P
(
X= x
1
) =
p
1
, P
(
X= x
2
) =
p
2
, …, P
(
X= x
n
) =
p
n
, respectively, then the
probability distribution of
X
may be expressed in the following way.
x
P
(
X = x
)
x
1
p
1
x
2
p
2
.
.
.
.
.
.
x
n
p
n
We can also graphically represent the probability distribution of a random variable.

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