C.3. Multiple Random VariablesWe often encounter several random variables that are related somehow. For example, a random signal as noise enters several circuits, and the outputs of these circuits can form multiple random variables . Multiple random variables are denoted by a vector X ={ X 1 , X 2 , ... X n }. C.3.1. Basic Functions of Two Random VariablesFor two random variables X and Y , the joint cumulative distribution function denoted by F X,Y ( x , y ), the joint probability mass function denoted by P X,Y ( x , y ), and the joint probability density function , f X, Y ( x , y ) are, respectively, derived from: Equation C.25
Equation C.26
and Equation C.27
We can define the marginal CDF of the two random variables as
Similarly, the marginal PMF of the two discrete random variables is
and the marginal PDF of the two continuous random variables is
C.3.2. Two Independent Random VariablesTwo random variables are considered independent of each other if one of the following corresponding conditions is met: Equation C.28
Equation C.29
or Equation C.30
|