The actuarially fair premium y0 E(y|N) is the expected annual amount that the insurance company pays me in claims. If my house is insured for $100,000 and = 0.001 (i.e. 0.1%), what is the actuarially fair premium per annum? What is the premium income for the insurer if the insurance company insures N people? Assuming 0.1% of policies give rise to claims, what is the expected cost of claims to the insurance company?