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Math Help - Expected value of a function depending on a r.v.

  1. #1
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    Expected value of a function depending on a r.v.

    If the number of accidents per day, Y, is assumed to have a Poisson distribution with mean 10, how can I find the expected cost to an insurance company per day, X, where X = 2000 - 3Y - Y^2?

    Thanks,

    Paul
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  2. #2
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    Quote Originally Posted by Canadian0469 View Post
    If the number of accidents per day, Y, is assumed to have a Poisson distribution with mean 10, how can I find the expected cost to an insurance company per day, X, where X = 2000 - 3Y - Y^2?

    Thanks,

    Paul
    E(X) = E(2000) - 3 E(Y) - E(Y^2) = 2000 - 3 (10) - E(Y^2).

    So the speed bump is getting E(Y^2). There are several ways of getting it. Here's the simplest:

    Recall that Var(Y) = E(Y^2) - [E(Y)]^2. You know Var(Y) and E(Y) so you can substitute and solve for E(Y^2).
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