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Suppose that X is nonnegative continuous random variable with
probability density function f_X(x).

Now, we have

A = Integral ( InverseLaplace(g*(s)) f_X(x), 0, INFINITE)

where Integral( ..., 0, INFINITE) represents the integral from zero to
positive infinite. InverseLaplace(g*(s)) represents the inverse
laplace of g*(s).

If A is greater(or less) than zero, then what condition should the
function g*(s)  satisfy ? Thank you very much for suggetions. Regards.

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