ACTSC432 Study Guide - Midterm Guide: Probability Mass Function, Mixture Distribution, Independent And Identically Distributed Random Variables

• School: University of Waterloo
• Department: Actuarial Science
• Course: ACTSC432
• Professor: Diana Parry

Document Summary

Id number : (10 marks) suppose that, conditional on (cid:2) = (cid:18), the rv(cid:146)s fxjgj(cid:21)1 are independent and identically distributed with common probability mass function pxj(cid:2) (xj(cid:18) ) = (cid:18)xe(cid:0)(cid:18) x! x = 0; 1; ::: We further assume that (cid:2) is a rv with the following two-point mixture density function (a) (3 marks) (cid:133)nd e [xj]. (cid:25)(cid:2) ((cid:18)) = p(cid:8)(cid:21)e(cid:0)(cid:21)(cid:18)(cid:9) + (1 (cid:0) p)(cid:8)(cid:21)2(cid:18)e(cid:0)(cid:21)(cid:18)(cid:9) , (cid:18) > 0. 1 (b) (4 marks) determine v ar (xj). 2 (c) (3 marks) (cid:133)nd cov (xi; xj) for i 6= j. 3: (12 marks) let x1; x2; :::; xn be the past total claims experience for a given policyholder. Under the number of claims basis, the american credibility factor z was found to be 0:45. All else being equal, (cid:133)nd the american credibility factor on the total amount of claims basis. 5: (8 marks) experienced runners have been categorized according to their group age and years of experience.