Joint Probability Density Function

[Hashmeer]

Homework Statement

X and Y are random variables with the joint density:

fXY(x,y) = k*e^(-lambda * x) if 0 < y < x < infinity
= 0, otherwise

Find P(X + 2*Y <= 3)

Homework Equations

I found k = lambda^2

The Attempt at a Solution

I'm not sure exactly how to solve this, but here are the ideas that I was starting to work off of:

1) Y = 0 since there is no function for y and you cannot solve for it in the original equation as it does not appear there.
2) If the above is true then the problem simplifies to P(X<= 3) which is a fairly simple thing to solve for.

I'm not sure if these are correct and have no way of checking my work, so I was hoping someone could confirm my thoughts or point me in the right direction.

Thanks!

 

[╔(σ_σ)╝]

Draw the region represented X+2Y < 3 and then integrate your pdf on that region. The region is some sort of triangle.

 

[Hashmeer]

Ah, right. Thanks for the help, that was pretty dumb...