Thread: Joint PDFs

Hi
I am really stuck on how to work out this maths problem. Could someone give me a bit of guidance on how to get it started.

Let f(x1, x2) = 4x1x2, 0 < x1 < 1, 0 < x2 < 1,
= 0 elsewhere.
I need to find this below

P(x1 = x2)


Thank you

Originally Posted by lh1188

Hi
I am really stuck on how to work out this maths problem. Could someone give me a bit of guidance on how to get it started.

Let f(x1, x2) = 4x1x2, 0 < x1 < 1, 0 < x2 < 1,
= 0 elsewhere.
I need to find this below

P(x1 = x2)


Thank you

The answer is zero and you should think about why ....

Are you sure the question wasn't something like find Pr(x1 < x2) ....?

That was the next question that we were given.

I have the answer to the question so I knew it was 0 but I do not know why.
For some reason we have limited information regarding this in our notes and as I have very limited statistical knowledge it is proving rather difficult to work out.
If you could give me a bit of guidance it would be very appreciated as I have an economics exam tomorrow!

Originally Posted by lh1188

That was the next question that we were given.

I have the answer to the question so I knew it was 0 but I do not know why.
For some reason we have limited information regarding this in our notes and as I have very limited statistical knowledge it is proving rather difficult to work out.
If you could give me a bit of guidance it would be very appreciated as I have an economics exam tomorrow!

Pr(X = a) = 0 for any continuous random variable .... (such will be somewhere in your classnotes and textbook).

Thank you for your help!

also by inspection the two rvs are independent with densities
2x1 and 2x2 on (0,1)