Joint problem density function problem

[Lewis7879]

I need help guys I can't understand this
Can anyone explain thoroughly how do I form the range for this question?
f(x,y)= e^-x for 0≤x≤y≤∞
0 Otherwise

Find P(x+y≤1)
I attempted this by integrating through the range of
0≤y≤(1-x) and 0≤x≤∞ but that doesn't seem right

 

[mathman]

The statement is confusing. You appear to have a density function in x and y, which is a function of x only.

 

[Lewis7879]

The statement is confusing. You appear to have a density function in x and y, which is a function of x only.

Hello mathman there's a slight error with range I made in the question which is 0≤y≤x≤∞
There was no other problems with the question as I was asked this way.

 

[HallsofIvy]

No, $f(x,y)= e^{-x}$ for $0\le x\le y\le A$ is a function of both x and y. To determine "A", use the fact that the "total" probability must be 1:
$$\int_{y= 0}^A\int_{x= 0}^y e^{-x} dx dy= 1$$

 

[mathman]

Getting an equation for A is easy enough. $A+e^{-A}=2$. I am confused as to what is the question.

 

[Lewis7879]

No, $f(x,y)= e^{-x}$ for $0\le x\le y\le A$ is a function of both x and y. To determine "A", use the fact that the "total" probability must be 1:
$$\int_{y= 0}^A\int_{x= 0}^y e^{-x} dx dy= 1$$

Will I be able to find P(x+y≤1) after determine A?