2011年4月CT3试卷.pdf

INSTITUTE AND FACULTY OF ACTUARIES EXAMINATION 15 April 2011 (pm) Subject CT3 — Probability and Mathematical Statistics Core Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and examination details as requested on the front of your answer booklet. 2. You must not start writing your answers in the booklet until instructed to do so by the supervisor. 3. Mark allocations are shown in brackets. 4. Attempt all 10 questions, beginning your answer to each question on a separate sheet. 5. Candidates should show calculations where this is appropriate. Graph paper is required for this paper. AT THE END OF THE EXAMINATION Hand in BOTH your answer booklet, with any additional sheets firmly attached, and this question paper. In addition to this paper you should have available the 2002 edition of the Formulae and Tables and your own electronic calculator from the approved list. CT3 A2011 © Institute and Faculty of Actuaries 1 The numbers of claims which have arisen in the last twelve years on 60 motor policies (continuously in force over this period) are shown (sorted) below: 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 5 5 5 5 6 6 6 7 Derive: (i) The sample median, mode and mean of the number of claims. [3] (ii) The sample inter-quartile range of the number of claims.