example

TRANSFORMING
RANDOM VARIABLES
of continuous type only (the less interesting discrete case was dealt with earlier).
The main issue of this chapter is: Given the distribution of X, find the distribution
of Y ? 1
1+X (an expression involving X). Since only one ’old’ RV variable
(namely X) appear in the definition of the ’new’ RV, we call this a univariate
transformation. Eventually, we must also deal with the so called bivariate transformations
of two ’old’ RVs (say X and Y ), to find the distribution of a ’new’
RV, say U ? X
X+Y (or any other expression involving X and Y ). Another simple
example of this bivariate type is finding the distribution of V ? X + Y (i.e. we
will finally learn how to add two random variables).TRANSFORMING
RANDOM VARIABLES
of continuous type only (the less interesting discrete case was dealt with earlier).
The main issue of this chapter is: Given the distribution of X, find the distribution
of Y ? 1
1+X (an expression involving X). Since only one ’old’ RV variable
(namely X) appear in the definition of the ’new’ RV, we call this a univariate
transformation. Eventually, we must also deal with the so called bivariate transformations
of two ’old’ RVs (say X and Y ), to find the distribution of a ’new’
RV, say U ? X
X+Y (or any other expression involving X and Y ). Another simple
example of this bivariate type is finding the distribution of V ? X + Y (i.e. we
will finally learn how to add two random variables).