E{N2} = 1000. The size of each individual claim from the rst group is 20 with probability 0.3, 40 with probability 0.4, and 100 with probability 0.3. The size of each individual claim from the second group is 40 with probability 0.4, and 100 with probability 0.6. Let N be the total number of claims, and let S be the total aggregate claim. Answer the questions 9-16. Question 9 4 pts Is it true that N follows the Poisson distribution with E {N} : 1500 and Var {N} : 1500? 0 True 0 False Question 10 10 pts Let Y; be the size of the ith claim arriving (whichever group it comes from). What's the distribution of K? O Y,- has mull-inornial distribution with parameter (1500;%,). O Y; has Poisson distribution with parameter 1500. O Y; equals 20, 40 and 100 with probabilities 0.1, 0.4 and 0.5 respectively. 0 Y, has Poisson distribution with parameter 160. O Y; equals 20, 40 and 100 with probabilities 0.15. 0.4 and 0.45 respectively. Question 11 10 pts Is it true that Sis a compound Poisson r.v. and can be written as S : Bill 1\"}? 6) True 0 False Question 12 15 pts Find E {S} and Var {S}. (Hint: Compute E {K} and E {K2} proceeding from the resuit of Question 10 and use Propositions 1* 2 that we proved in class regarding E {S} and Var {S} in the case where N is a Poisson 11v.) 0 E{S} = 102000 and Var {S} = 3520000 0 E{S} = 96000 and Var {S} = 1656000 0 E{S} = 102000 and Var {S} = 1534000 0 E{S} = 96000 and Var{.5'} : 7300000