1) a) State and prove the Law of large numbers. That is if X1, X2, . . . are i.i.d. then the average on the long run converges to . ? Explain why. b) Explain why for a sequence of i.i.d. X1, X2, . .., we have "XitXat..+Xn = Vnox,. c) The yearly insurance claims for car insurance of the ith customer is denoted by X;. We assume X1, X2, ... are i.i.d. The expected cost of a claim is E[X,] = 1000. The standard deviation is OX = 3000 If the insurance has 10000 people insured, and no other insurance contracts, how much does the insurance need to charge each client to cover the yearly total claim with probability 0.975 at least. (not including profit and administrative cost)