P_PracticeExam6_05-1..

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SECTION 10 22. A random variable X has the log-normal distribution with the density: 1 ( ln x# µ )2 fX ( x) = 1 2 " e# x 2! for x > 0, and 0 otherwise, where µ is a constant. You are given that Pr X ! 2 E( X). ( ) = 0.4. Find A. 4.25 B. 4.66 C. 4.75 D. 5.00 E. Cannot be determined 23. You are given a continuous random variable with the density fX ( x) = 1 2 x + 1 2 for !1 " x " 1, and 0 otherwise. Find the density of Y = X 2 , for all points where that density is nonzero. A. 1 3 B. 2y C. 2 y 2y 4 D. 3 y2 E. 1 yln2 24. An insurer has 10 independent one-year term life insurance policies. The face amount of each policy is 1000. The probability of a claim occurring in the year under consideration is 0.1. Find the probability that the insurer will pay more than the total expected claim for the year. A. 0.01 B. 0.10 C. 0.16 D. 0.26 E. 0.31 25. An insurance policy is being issued for a loss with the following discrete distribution: ! 2, with probability 0.4, X = " # 20, with probability 0.6. Your job as the actuary is to set up a deductible d for this policy so that the expected payment by the insurer is 6. Find the deductible. A. 1 B. 5 C. 7 D. 10 E. 15 26. For a Poisson random variable N with mean ! find lim E( N N # 1). !"0 A. ! B. 0 C. 1 D. e E. Cannot be determined ASM Study Manual for Course P/1 Actuarial Examination. © Copyright 2004-2007 by Krzysztof Ostaszewski - 256 -
PRACTICE EXAMINATION NO. 6 27. X is a normal random variable with mean zero and variance 1 and Y is distributed 2 exponentially with mean 1. X and Y are independent. Find the probability Pr Y > X 2 ( ). 1 e A. B. C. e ! 28. ( 1 ) , X ( 2) , , X ( 400) 1 1 2 D. E. 2! 2 2 X … are order statistics from a continuous probability distribution with a finite mean, median m and variance ! 2 . Let ! be the cumulative distribution function of the Pr X ! m ( ) standard normal distribution. Which of the following is the best approximation of ( 220) using the Central Limit Theorem? & 20 # A. ! ( 0.05" ) B. 0.0049 C. 0.0532 D. 0.0256 E. ' $ ! % ( " 29. N is a Poisson random variable such that Pr( N ! 1) = 2 " Pr( N = 2). Find the variance of N. A. 0.512 B. 1.121 C. 1.618 D. 3.250 E. 5.000 30. There are two bowls with play chips. The chips in the first bowl are numbered 1, 2, 3, …, 10, while the chips in the second bowl are numbered 6, 7, 8, …, 25. One chip is chosen randomly from each bowl, and the numbers on the two chips so obtained are compared. What is the probability that the two numbers are equal? 1 1 1 1 1 A. B. C. D. E. 2 5 10 40 50 ASM Study Manual for Course P/1 Actuarial Examination. © Copyright 2004-2007 by Krzysztof Ostaszewski - 257 -
Page 1 and 2: PRACTICE EXAMINATION NUMBER 6 1. An
Page 3 and 4: ! 1 $ A. # & " # ! % & B. ! 1 $ # &
Page 5: PRACTICE EXAMINATION NO. 6 17. The
Page 9 and 10: We have: 40 " ( ) !2 1 = C 10 + x 0
Page 11 and 12: with density function ! 2x, for 0 <
Page 13 and 14: PRACTICE EXAMINATION NO. 6 ! 4 1.5
Page 15 and 16: PRACTICE EXAMINATION NO. 6 Let W =
Page 17 and 18: "# PRACTICE EXAMINATION NO. 6 The d
Page 19 and 20: 20 ! z 10 PRACTICE EXAMINATION NO.
Page 21 and 22: Similarly, Pr X( 7) < m PRACTICE EX
Page 23 and 24: This density at 1 ! 1$ , " # 2 2% &
Page 25 and 26: The survival function for the Weibu
Page 27 and 28: PRACTICE EXAMINATION NO. 6 21. Let
Page 29 and 30: PRACTICE EXAMINATION NO. 6 Let z0.6
Page 31 and 32: 26. For a Poisson random variable N
Page 33: Find the variance of N. A. 0.512 B.

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