1. Consider the following nonnegative absolutely continuous probability distribution which belongs to the family that is frequently used to model claim size because its "heavy tail captures the risk of unexpected large claims quite well. This distribution is characterized by its cumulative distribution function F(x)=\left\{\begin{array}{ll} 0 & \text { for } x<0 \\ 1-1 /(1+x)^{2} & \text { for } x \geq 0 \end{array}\right. Determine the expected value of this distribution.

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