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Help with joint pdf problem from actex 2009

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  • Help with joint pdf problem from actex 2009

    Hi I am new to the forum and would greatly appreciate any help with this problem I am having. The problem states:

    An insurance company insures a large number of drivers. Let X be the random variable representing the company's losses under collision insurance, and let Y represent the company's losses under liability insurance. X and Y have joint density function

    f(x,y)= (2x+2-y)/4 for 0<x<1 0<y<2

    What is the probability that the total loss is at least 1?

    I completely understand the explanation they give but if you attempt the problem by getting the complement which would be 1-P(X+Y<1) the answer comes out to be .75, where the actual answer is .71. Any thoughts? Thanks

  • #2
    Originally posted by shong85 View Post
    Hi I am new to the forum and would greatly appreciate any help with this problem I am having. The problem states:

    An insurance company insures a large number of drivers. Let X be the random variable representing the company's losses under collision insurance, and let Y represent the company's losses under liability insurance. X and Y have joint density function

    f(x,y)= (2x+2-y)/4 for 0<x<1 0<y<2

    What is the probability that the total loss is at least 1?

    I completely understand the explanation they give but if you attempt the problem by getting the complement which would be 1-P(X+Y<1) the answer comes out to be .75, where the actual answer is .71. Any thoughts? Thanks
    It works, check your math.
    On the integral from 0 to 1-x you get:
    -5/8x^2 + 1/4x + 3/8

    Integrate that, you get
    -5/24 + 1/8 + 3/8 = .29
    1-.29 = .71

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