View Single Post
cse63146
cse63146 is offline
#1
Mar22-09, 07:50 PM
P: 452
1. The problem statement, all variables and given/known data

Let X and Y be continuous random variables having joint probability density function

[tex]f(x,y) = e^{-y}[/tex] if 0 [tex]\leq x \leq y[/tex]

A) Determine the joint cumulative distribution function F(x,y) of X and Y. (Hint: Consider the three cases 1) [tex]x \leq 0[/tex] or [tex]y \leq 0[/tex] 2) 0 < x < y 3) 0 <y < x

B) Let [tex]F_X (x)[/tex] and [tex]F_Y (y)[/tex] be the marginal cumulative distribution functions of X and Y. One can show that [tex]F_X (x) = Lim_{Y \rightarrow \infty} F(x,y)[/tex] and [tex]F_Y (y) = Lim_{X \rightarrow \infty} F(x,y)[/tex]. Use this result to obtain [tex]F_X (x)[/tex] and [tex]F_Y (y)[/tex]
2. Relevant equations



3. The attempt at a solution

Not sure how to start with A).

I know that [tex] F(x,y) = \int^x_{- \infty} \int^y_{- \infty} f(x,y) dy dx[/tex]

Does it mean for the case where x < 0 it would be:

[tex] F(x,y) = \int^0_{- \infty} \int^y_{- \infty} f(x,y) dy dx[/tex] ?
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes