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Practice Questions 3

# Practice Questions 3 - Practice Questions 3 ACTSC 431/831...

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Practice Questions 3 – ACTSC 431/831, FALL 2011 1. The conditional hazard rate function of loss X , given Λ = λ , is h ( x | λ ) = λx 3 . The distribution of Λ is a gamma distribution G (2 , 4). (a) Calculate the probability that the loss is less than one. (b) Justify if the distribution of X is DFR, or IFR, or neither. (c) Compare the distribution of loss X with that of loss X 4 to determine whether or not one loss has a heavier tail than the other. 2. Let loss X have a three-component spliced distribution. The pdf of X has the following form: f X ( x ) = 0 , x < 0 , 0 . 06 , 0 x < 5 , 0 . 1 , 5 x < 10 , a x 4 , x 10 . (a) Calculate the variance of the loss. (b) Calculate the distribution function F X ( x ) of the loss for all x ( -∞ , ). (c) Calculate the probability that the loss is between 4 and 8. 3. Let N be the number of claims in an insurance portfolio. The sizes of claims in the portfolio are i.i.d. random variables with common

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Practice Questions 3 - Practice Questions 3 ACTSC 431/831...

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