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days of hospitalization,X, is a discrete random variable with probability function p_{X}(k)=\left\{\begin{array}{cc} \frac{6-k}{15} & \text { for } k=1,2,3,4,5 \\ 0 & \text { otherwise } \end{array}\right. (a) (5 points) Determine the expected payment for hospitalization under this policy. (b) (5 points) Determine the variance of the payment for hospitalization under this policy.

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