Question

Two random variables X and Y have a constant joint density function f ( x,y ) = c in the domain ( x < 10 < x > y > 0 )(and zero elsewhere).

(a) Find c .

(b) Find P ( X - Y < 4).

(c) Find P( X - Y = 1 )

(d) Find P(X^2 + Y^2 < 4).

Are X and Y independent? Explain

Answer 1

Hints:
1. The non-zero region is a triangle.
2. Integral of f(x,y) over the region is 1 (because f(x,y) is a joint probability function).

If you need help with double integrals, try for example:
http://mathematiques.brinkster.net/

Answer 2

Thanks

Answer 3

You're welcome!