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Math Help - Joint density problem

  1. #1
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    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?

    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
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  2. #2
    MHF Contributor matheagle's Avatar
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    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
    Last edited by matheagle; June 21st 2011 at 03:09 PM.
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  3. #3
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    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.
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