I am stuck with the problem below:
The Joint pdf of random variables X and Y: f(x,y) = k/y , 0<x<y, 0<y<1 and f(x,y) = 0, otherwise.
First of all, the question asked to draw a diagram showing the support of the joint pdf.
Probably this is the part that i am unable to do, which leads to problems with later part of the question.
The question asked to calculate k, I integrate with respect to x over the range 0 to y, and then integrate with respect to y over the range 0 to 1.
The answer I get is k = 1, is it correct? Did i integrate the correct range for x and y?
After that the question asked to find: P(0<=X<=1/4, 0<=Y<=1/3).
For X, the range i used to integrate over function f is 0 to 1/4. However, for Y, i am not so sure about it, I guess it is from 1/4 to 1/3? Or 0 to 1/3 for Y?
Any help regarding the problem would be appreciated.
The integral you're expected to set up and solve is . Then equate the result of this calculation to 1 in order to solve for k.
Yes, i have been taught how to do double integral over x-y plane. I also prefer the lower bounds to be set to zero too, much easier..Thanks Matheagle.
Been quite confuse in deciding the range for integration.
Thanks a lot of clarified my doubts.
As for the last part: Finding P(0<=X<=1/4, 0<=Y<=1/3).
The integration will look like this: ?
If i wish to integrate by dxdy, range of x will be from 0 to 1/4. How about y? ?