# joint pdf

• Nov 10th 2008, 12:42 AM
kaupehkaubu
joint pdf
Hi, i have been given such pdf

f(x,y) = k/y, 0<x<y, 0<y<1
f(x,y) = 0 elsewhere

How should i construct in order to find k?
• Nov 10th 2008, 02:08 AM
mr fantastic
Quote:

Originally Posted by kaupehkaubu
Hi, i have been given such pdf

f(x,y) = k/y, 0<x<y, 0<y<1
f(x,y) = 0 elsewhere

How should i construct in order to find k?

Quote:

Originally Posted by CaptainBlack
For this problem your best policy is to draw a diagram (makes a mystic symbol in the air to ward of the wrath of Bourbaki).

[snip]

Have you applied this advice here? If so, it should be clear that you require the value of k such that $\displaystyle \int_{x=0}^{x=1} \int_{y=x}^{y=1} \frac{k}{y} \, dy \, dx = 1$.

But if you reverse the order of integration the calculation is much simpler ....
• Nov 10th 2008, 02:29 AM
kaupehkaubu
So if I reverse the order, am I going to get this?

$\displaystyle \int_{y=0}^{y=1} \int_{x=0}^{x=y} \frac{k}{y} \, dx \, dy = 1$
• Nov 10th 2008, 03:03 AM
mr fantastic
Quote:

Originally Posted by kaupehkaubu
So if I reverse the order, am I going to get this?

$\displaystyle \int_{y=0}^{y=1} \int_{x=0}^{x=y} \frac{k}{y} \, dx \, dy = 1$

Yes.