Joint density problem

**lindah** · June 21st 2011, 02:37 AM

May I obtain critiques/hints/tips on my approach?

Q1) I evaluated the double integral and it was equal to 1. I also substituted x=10, 20 into the function and confirmed it is >0
$\int_{10}^{20} \int_{x/2}^{x} \frac{20-x}{25x}\ dydx$

Q2) I drew the graph for limits of integration

For the marginal density of x I have:
$\int_{x/2}^{x} \frac{20-x}{25x}\ dy = \frac{20-x}{50}$

For the marginal density of y I have:
$\int_{10}^{2y} \frac{20-x}{25x}\ dx + \int_{y}^{20} \frac{20-x}{25x}\ dx$
May I ask if my bounds correct in calculating this?

Q3) I had:
$\frac{20-x}{25x} \times \frac{50}{20-x} = \frac{2}{x}$

Q4) I feel it is related to Q3, and wanted to see if I have Q3 correct first

**matheagle** · June 21st 2011, 08:03 AM

those bounds are correct, they are two triangles
it's good to see that you drew the region
otherwise it's nearly impossible to figure out the bounds

**lindah** · June 21st 2011, 02:36 PM

Thanks for checking it!
I originally put in the bounds as [10,20] and obtained a scalar for the answer and thought that was very odd.

Thread: Joint density problem

LinkBack

Thread Tools

Display

Joint density problem

Re: Joint density problem

Re: Joint density problem

Similar Math Help Forum Discussions

Joint density problem: what am I doing wrong?

Joint Density Problem

[SOLVED] joint density function /joint probability

Joint Density Problem Help!

Joint Density problem....

Search Tags