Joint density problem

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• Jun 21st 2011, 03:37 AM
lindah
Joint density problem
http://img690.imageshack.us/img690/3075/61270887.png
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
• Jun 21st 2011, 09:03 AM
matheagle
Re: Joint density problem
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
• Jun 21st 2011, 03:36 PM
lindah
Re: Joint density problem
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.