Advanced Mathematics

6. (10 points total) An insurance policy pays $1000 per day for up to 3 days of hospitalization and$500 per day for each day of hospitalization thereafter. The number of 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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