Joint Discrete Distributions
It is often of interest to consider probabilities for more than
one random variable at a time. For example,
X
1
is the
height of a man (inches),
X
2
is the height of his son
(inches), we are interested in
P
(
X
2
≤
60

60
≤
X
1
≤
61)
.
Definition 1.
A
k
dimensional
random vector
is a function from
S
(sample space) to
R
k
. We may denote it as
X
= (
X
1
, . . . , X
k
)
, where
X
i
s are a random variables; or
(
X, Y, Z, . . .
)
.
Chapter 4 Joint Distributions  p. 2/133