1. ## Joint density problem

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?

$\frac{20-x}{25x} \times \frac{50}{20-x} = \frac{2}{x}$

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

2. ## 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

3. ## 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.