# Describe how buying of insurance affects the profit, its expected value and variance? Does buying insurance is cost-efficient in the long run? In which case Space Company Z can decide to buy insurance and why?

Space Company Z is preparing to launch a spaceship. If the launch is successful, the company earns $100 million in profit. In case of failure, the company loses $200 million (i.e. negative profit). Probability of failure is 1/10. The company can buy insurance for this launch. Cost of insurance is $30 million (paid before the launch). In case of failure the insurer will pay Space Company Z $200 million (thus compensating all the damages). Consider two cases: 1. Space Company Z decided not to buy insurance. 2. Space Company Z decided to buy insurance. Denote its profit in the first case by X and in the second case by Y. (In the second case profit includes payments to/from the insurer taken with appropriate sign.) Find expected values and variances of X and Y. Describe how buying of insurance affects the profit, its expected value and variance? Does buying insurance is cost-efficient in the long run? In which case Space Company Z can decide to buy insurance and why? Space Company Z is preparing to launch a spaceship. If the launch is successful, the company earns $100 million in profit. In case of failure, the company loses $200 million (i.e. negative profit). Probability of failure is 1/10. The company can buy insurance for this launch. Cost of insurance is $30 million (paid before the launch). In case of failure the insurer will pay Space Company Z $200 million (thus compensating all the damages). Consider two cases: 1. Space Company Z decided not to buy insurance. 2. Space Company Z decided to buy insurance. Denote its profit in the first case by X and in the second case by Y. (In the second case profit includes payments to/from the insurer taken with appropriate sign.) Find expected values and variances of X and Y. Describe how buying of insurance affects the profit, its expected value and variance? Does buying insurance is cost-efficient in the long run? In which case Space Company Z can decide to buy insurance and why