# Thread: X and Y have following joint CDF: ? 3 questions

1. ## X and Y have following joint CDF: ? 3 questions

Suppose that X and Y have the following joint cumulative distribution function:

F(x,y) = [1 - e^(-2x)] [1 - e^(-3y)] I(0,infinite)[x], I(0,infinite)[y]

i. What does lim (y goes to infinite) F(2,y) denote?

ii. What does lim (y goes to infinite) F(2,y) equal?

iii. Find the joint probability density function fX,Y for X and Y.

Any help with this problem will be appreciated. part iii in particular. thanks

2. Originally Posted by plm2e
Suppose that X and Y have the following joint cumulative distribution function:

F(x,y) = [1 - e^(-2x)] [1 - e^(-3y)] I(0,infinite)[x], I(0,infinite)[y]

Sorry but I don't understand your notation. In particular, what does I(0,infinite)[x], I(0,infinite)[y] mean?

3. x goes from 0 to infinity, y goes from zero to infinity

4. Originally Posted by plm2e
x goes from 0 to infinity, y goes from zero to infinity
What is being integrated? If you're integrating [1 - e^(-2x)] [1 - e^(-3y)] from x goes from 0 to infinity and y goes from zero to infinity then this does not define a joint cumulative distribution function.

What you've posted still makes no sense (to me, anyway).