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help needed with a question.

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  • help needed with a question.

    hey folks i really dont know how to approach this ques i would really appreciate some assistance

    [SOA/CAS 1999 Practice Exam # 37] An insurance contract reimburses a family’s automobile
    accident losses up to a maximum of two accidents per year. The joint probability
    distribution for the number of accidents of a three person family (X, Y,Z) is
    p(x, y, z) = k(x + 2y + z)
    where x = 0, 1, y = 0, 1, 2, z = 0, 1, 2 and x, y and z are the number of accidents incurred by
    X, Y and Z, respectively.
    Determine the expected number of unreimbursed accident losses given that X is not involved
    in any accidents.

  • #2
    1. There are 3x3x3 = 27 possible combinations; the sum of the probabilities of those combinations equals 1. Thus, plug in the values in p(x,y,z) and solve for k.
    2. If X is not involved in any accidents, you know what x has to be.
    3. Given that fact, calculate the probability of X not having any accidents [how many possibilities are there?]
    4. Given that fact, what's the probability of having 3 or more accidents?
    "You better get to living, because dying's a pain in the ***." - Frank Sinatra - where I talk about the Blues and the NHL.