By Ph.D., ASA Samuel A. Broverman

ISBN-10: 1566988969

ISBN-13: 9781566988964

The ACTEX C/4 examine guide is the right learn software to assist within the education for the SOA examination C and CAS examination four. It presents thorough assurance of the entire syllabus issues of modeling, version estimation, version building and choice, credibility, simulation and danger measures.

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785 . We are asked to find P[8 = IIX > 2000]. It is generally the case that to find a conditional probability we use the basic definition of conditional probability. P[8 - IIX - > 2000] - P[(8=I)n(X>2000)J - P[X>2000] · We apply the usual probability rules to find the numerator and denominator. 5) (since X has an exponential distribution with mean 1000 if 8 =I). P[(8 =I) P[X > 2000] = P[(X > 2000) n (8 =I)]+ P[(X > 2000) n (8 =II)]. We have already found the first term on the right hand side of this expression.

Ii) Individual claim size amounts are independent and exponentially distributed with mean 5000. 90. Using classical credibility, determine the expected number of claims required for full credibility. A) 2165 © ACTEX2012 B) 2381 C) 3514 D) 7216 E) 7938 SOA Exam C/CAS Exam 4 - Construction and Evaluation of Actuarial Models CR-22 21. CREDIBILITY- PROBLEM SET 1 (SOA) You are given: (i) The number of claims has a Poisson distribution. 5 and a= 6. (iii) The number of claims and claim sizes are independent.

71 (SOA May 07) The observation from a single experiment has distribution: Pr(D =diG= g)= g(l-d)(l- g)d for d = 0,1 The prior distribution of G is: Pr(G = ~) = ~ and Pr(G = ~) = ~ Calculate Pr(G = ~ID = 0). E) 10 19 © ACTEX2012 SOA Exam C/CAS Exam 4- Construction and Evaluation of Actuarial Models CREDIBILITY - PROBLEM SET 2 CR-45 CREDIBILITY- PROBLEM SET 2 SOLUTIONS 1. + P[redlbowl2]· P[bowl2] P[red] = P[redlbowll] · P[bowll] Answer: C 5 = ( 10 )( ~) 2. ) _ §. P[b owIll re dl -- P[bowllnred] P[red] 7/20 7/20 - 7 · 3.

### ACTEX C/4 study manual by Ph.D., ASA Samuel A. Broverman

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