Page 94 - Schaum's Outlines - Probability, Random Variables And Random Processes

CHAP. 31 MULTIPLE RANDOM VARIABLES

Conditional pmf's are defined similarly. For example,

A continuous n-variate r.v. will be described by a joint pdf defined by

Then

and

.
.
Properties of fx, . &(xi, . . . , x,) :

The marginal pdf's of one or more of the r.v.'s are obtained by integrating Eq. (3.72) appropriately.
For example,

Conditional pdf's are defined similarly. For example,

The r.v.'s XI, . . . , Xn are said to be mutually independent if

for the discrete case, and

for the continuous case.
The mean (or expectation) of Xi in (XI, . . . , Xn) is defined as

C . 1 xipxl ..xn(xl, .--, xn) (discrete case)
(3.82)
.
.
xi fX1 ... X,(~l, . , x,) dxl . dxn (continuous case)
The variance of Xi is defined as