**Mumbai University > Electronics and Telecommunication Engineering > Sem 5 > Random Signal Analysis

Marks: 10M

Year: May 2016

Let $f_{XY}$ (x,y) be joint probability density function of (X, Y)

We introduce auxillary random variable W=Y

Now we have Z=X+Y and W=Y i.e z=x+y and w=y

∴x=z-y =z-w and y=w

∴J=

∴J= =1

We know the joint probability density function $f_{ZW}$ (z,w)=|J| $f_{XY}$ (x,y)=$f_{XY}$ (x,y)

Since X …