We have an inhomogeneous spatial poisson process and several point (x,y). Let the intensity be
$$lambda (x,y)=constant*e^{x-y}$$. What is then the corresponding f(x,y)? How do we sample from this distribution? What property of f(x,y) and the relation between the corresponding stochastic variables X and Y are you using?

We also know that $$f(x,y)=\lambda (x,y)/\lambda$$ where lambda is the integral for $$\int_{W}^{} \lambda (x,y)$$
W=[1,0]x[0,1].

Question

We have an inhomogeneous spatial poisson process and several point (x,y). Let the intensity be 
$$lambda (x,y)=constant*e^{x-y}$$. What is then the corresponding f(x,y)? How do we sample from this distribution? What property of f(x,y) and the relation between the corresponding stochastic variables X and Y are you using?

We also know that $$f(x,y)=\lambda (x,y)/\lambda$$ where lambda is the integral for $$\int_{W}^{} \lambda (x,y)$$ 
W=[1,0]x[0,1].

abb0t · Answer

Whoa, is this for engineering statistics?

anonymous · Answer

Yes. Yes it is.

abb0t · Answer

Yeah, I thought so. I sat through a course just to see and I remember seeing spatial poisson process. I don't think I know of any aerospace or electrical engineers on this site who can help, MAYBE @Frostbite can help. But this course is upper division almost grad-level course.
Best of luck though. 

Cheers.

frostbite · Answer

@abb0t I suppect you begin to hate me... I'm just a little bachelor baby student ;/ ... and especially not an engineer.

abb0t · Answer

Lol. No I don't. Some chemical engineers take upper-division statistics which is why I thought you may be familiar :3 
I heard about this course tho, it's supposed to be really tough!

frostbite · Answer

@amistre64 might just know.

amistre64 · Answer

my casio from 1973 only goes up to division :)

amistre64 · Answer

i see that W is a region across which to integrate, but determine the f(x,y) is a little out of my sights