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Math Help - finding second moment?

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    Thumbs down finding second moment?

    An insured person is three times more likely to file exactly two claims than to file exactly three claims. Assume that the number X of claims filed has a Poisson distribution. how do you find E[X^2] ??
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    Quote Originally Posted by Statsnoob2718 View Post
    An insured person is three times more likely to file exactly two claims than to file exactly three claims. Assume that the number X of claims filed has a Poisson distribution. how do you find E[X^2] ??
    \Pr(X = 2) = 3 \Pr(X = 3) \Rightarrow \frac{e^{-\lambda} \lambda^2}{2!} = \frac{3 e^{-\lambda} \lambda^3}{3!} \Rightarrow \lambda^2 = \lambda^3. Solve for \lambda.

    Now note that E(X^2) - [E(X)]^2 = Var(X). And you should know that E(X) = Var(X) = \lambda ....
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