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    Probability density function for cost

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    The actual cost of a system, X, in $50,000, is predicted by the probability density function
    f(x) = { 0.5 - |0.5-0.25x| for 0 <= x <= 4 and 0 otherwise

    1. What is the expected cost to system?
    2. What is the cost Xs of system for which the probability of exceeding Xs is 0.01?

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    Solution Preview

    f(x) ={ 0.5 - |0.5-0.25x| for 0 <= x <= 4 and 0 otherwise
    OR

    f(x) =
    0.5 - 0.5+0.25x == 0.25x for 0 <= x < 2
    and
    0.5 + 0.5 - 0.25x == 1.0 - 0.25x for 2 <= x <= 4
    and
    0 otherwise

    1.
    E(X) = integration(0 to 4) {x.f(x).dx}
    => E(X) = integration(0 to 2) {x.f(x).dx} + integration(2 to 4) {x.f(x).dx}
    => E(X) = ...

    Solution Summary

    For given probability density function, expected cost is estimated. Also, for given probability, cost is estimated.

    $2.19

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