Let X and Y be independent, uniform r.v's in (-1, 1). Compute the pdf of V=$(X+Y)^2 $

Mumbai University > Electronics and Telecommunication > Sem5 > Random Signal Analysis

Marks: 5M

Year: May 2015

Given V=${(X+Y)}^2$

∴ $\sqrt v=$x+y and u=y

∴ $x=\sqrt v-u$

Also X, Y is independent uniform random variables

$$ i.e f_X (x)=\frac{1}2 .... -1≤x≤1$$

$$ =0 $$

$$ f_Y (y)=\frac{1}2 ... -1≤y≤1$$

$$∴f_{XY} (x,y )=f_X (x)×f_Y (y)=1/4 .... -1≤x,y≤1$$

$$ ∴ J=\begin{vmatrix} \frac{δx}{δu} & \frac{δx}{δv} \\\\ \ \frac{δy}{δu} & {δy}{δv} …