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Math Help - Mean and variance with parameter

  1. #1
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    Mean and variance with parameter

    I am having trouble with this particular problem and could use some help.

    Let N be accidents that occur in a year and it is a Poisson distribution with parameter t.
    S = X1 + X2 + ... + Xn where Xi is the amount of the insurance claim for the accident. Xi are iid with a mean "u" and variance "o^2"

    How do you find the mean and variance of S?
    Mean is n * u and variance n * (o^2)
    But N is poisson so this varies?
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  2. #2
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    Quote Originally Posted by cubs3205 View Post
    I am having trouble with this particular problem and could use some help.

    Let N be accidents that occur in a year and it is a Poisson distribution with parameter t.
    S = X1 + X2 + ... + Xn where Xi is the amount of the insurance claim for the accident. Xi are iid with a mean "u" and variance "o^2"

    How do you find the mean and variance of S?
    Mean is n * u and variance n * (o^2)
    But N is poisson so this varies?
    Try using Wald's equation: Wald's equation - Wikipedia, the free encyclopedia
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