Question

Let X and Y be continuous and independent random variables, both with uniform distribution (0,1). Find the functions of probability densities of

(a) X + Y

(b) X-Y

(c) | X-Y |

Answer 1

Solution :
We have れD0ð. V x and y are independen Le 2 2 2- Therefore gethe Joint pdf of (u, v) Xy u-y utV arc indepe- Xand ndent 2

The graphical representa ion of Support oF五(UU) įs u) IS 21 1,-1) we heve he joint Pof of X (U,x) ex ( ur) other ω16e The morgin od pdt of u is Lu

uC2 end for 2-u U)스 녀-1 Νο», the marginal Pdf OF V IS 2 2-V 2 b) The distnbution 있 V. X. Y is otherwise