Suppose X and Y are jointly distributed random variables wit

Suppose X and Y are jointly distributed random variables with density,

f(x,y)=C, 0>x>y>1. Find C.

Answer : C = 2

Solution:

X and Y are jointly distributed random variables .

Therefore,

integral (0<x<1)(0<y<x) f(x,y) dydx = 1

=> integral (0<x<1)(0<y<x) C dydx =1

=> integral (0<x<1)(0<y<x) Cy dx =1

=> integral (0<x<1) Cx dx =1

=> (0<x<1) Cx^2/2 =1

=> C/2 =1

=> C = 2 Answer