In the health insurance example introduced in Example 3.6, the largest annual expense for the annual employee \((\$ 1,108)\) was caused by 8 visits to a provider for a knee injury requiring physical therapy. The couple has confidence that this or a similar injury will not happen again in the coming year, and wonders about the effect of reduced visits on expected total health care costs and its variability. A new joint distribution of health care cost for the couple is shown in the following table:

(a) For the partner, will there be a change to the expected cost and its standard deviation?

(b) Calculated the expected value and standard deviation for the employee's costs.

(c) Calculate the expected total cost for the couple.

(d) Calculate the new correlation for employee and partner costs.

(e) Calculate the standard deviation of the total cost.

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Partner costs, Y Employee costs, X $968 $988 $968 0.18 0.12 $1,008 0.15 0.25 $1,028 0.07 0.23