It's from the "loss analysis" course for your reference.

We consider an insurance covering a certain risk. It is given that loss amount of each risk has exponential distribution with mean 1125.3. The insurance has an ordinary deductible d. Suppose that the insurance company has doubled the amount of deductible in the policy, it is found that expected cost per loss will be halved after the adjustment. Questions (a) Calculate the loss elimination ratio after the adjustment. (b) Calculate the minimum value of x such that there is at least 98% probability that the claim payment made by the company is less than x when a claim request is received from the policyholder. We consider an insurance covering a certain risk. It is given that loss amount of each risk has exponential distribution with mean 1125.3. The insurance has an ordinary deductible d. Suppose that the insurance company has doubled the amount of deductible in the policy, it is found that expected cost per loss will be halved after the adjustment. Questions (a) Calculate the loss elimination ratio after the adjustment. (b) Calculate the minimum value of x such that there is at least 98% probability that the claim payment made by the company is less than x when a claim request is received from the policyholder