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Math Help - Maths help?! question about joint density functions and insurance

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    Post Maths help?! question about joint density functions and insurance

    A company is reviewing tornado damage claims under a farm insurance policy. Let X be the portion of a claim representing damage to the house and let Y be the portion of the same claim representing damage to the rest of the property. The joint density function of X and Y is

    f (x,y) = 6 [1 - (x + y)] for x > 0, y > 0, x + y < 1
    and 0 elsewhere

    how do you determine the probability that the portion of a claim representing damage to the house is less than 0.2 ? thank you for your time
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    Quote Originally Posted by Statsnoob2718 View Post
    A company is reviewing tornado damage claims under a farm insurance policy. Let X be the portion of a claim representing damage to the house and let Y be the portion of the same claim representing damage to the rest of the property. The joint density function of X and Y is

    f (x,y) = 6 [1 - (x + y)] for x > 0, y > 0, x + y < 1
    and 0 elsewhere

    how do you determine the probability that the portion of a claim representing damage to the house is less than 0.2 ? thank you for your time
    Draw the region defined by the support. Then it should be clear to you that \Pr(X < 0.2) = \int_{x = 0}^{x = 0.2} \int_{y = 0}^{y = 1-x} f(x, y) \, dy \, dx.
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