By by Abraham Weishaus.
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B) 1 (D) 4 (C) 2 (E) 6 (4B-S95:28] (2 points) You are given the following: • For any random variable X with finite first three moments, the skewness of the distribution of X is denoted Sk(X). X and Y are independent, identically distributed random variables with mean= 0 and finite second and third moments. • Which of the following statements must be true? 1. 2 Sk(X) = Sk(2X) 2. -Sk(Y)= Sk(-Y) 3. ISk(X)I ~ ISk(X + Y)l (A) 2 (B) 3 (C) 1,2 (D) 2,3 (E) None of A, B, C, or D l ' C/ 4 Study Manual- II th edition Copyright ©2010 ASM Exercises continue on the next page ...
Using the Loss Models tables, we have E[Xk] = Bk(a+ k -1) .. ·a. So J1 =200 Jl; = 60000 Jl~ =24 ·10 a 2 = 60000 - 200 2 = 20000 6 Jl~ = 120 ·10 8 /14 = 108 ( 120- 4(24)(2) + 6(6)(2 2) - 3(2 4 )) = 24 ·10 8 _ 24 ·10 -f6l 4·l0a -~ 8 r2C/4 Study Manual-!! th edition Copyright ©2010 ASM 20 1. 5. The distribution is symmetric, so its skewness is@]. (B) If this is not obvious to you, calculate the mean, which is 300. L 3 divided by a 3 , is 0. 6. a2 =a£J2 J1 = a£J a 1 1=-=-=>a=1 J1 0 3 (1)(2)(3)- 30 3 (1)(2) + 20 3 (1 3 } Y1 = (Cl)(£J2) ra t/2 = 6-~+2 = 0 (C) 1.
3-F01:37] For watches produced by a certain manufacturer: (i) Lifetimes follow a single-parameter Pareto distribution with a> 1 and B = 4. (ii) The expected lifetime of a watch is 8 years. Calculate the probability that the lifetime of a watch is at least 6 years. 67 Exercises continue on tile next page ... 16 1. 12. [4B-F99:29] (2 points) You are given the following: • A is a random variable with mean 5 and coefficient of variation 1. B is a random variable with mean 5 and coefficient of variation 1.
A.S.M. study manual for Exam C/exam 4 : construction and evaluation of actuarial models by by Abraham Weishaus.