{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Practice Questions 2

Practice Questions 2 - Practice Questions 2 ACTSC 431/831...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Practice Questions 2 – ACTSC 431/831, FALL 2011 1. Suppose that loss Y has a two-point mixture distribution with the following cdf: F Y ( y ) = 0 . 2 F 1 ( y ) + 0 . 8 F 2 ( y ) for all y, where F 1 ( y ) and F 2 ( y ) are the distribution functions of 1 X and e X , respectively. Here, X has a gamma distribution G (2 , 1 / 4). Hence, F 1 ( y ) and F 2 ( y ) are inverse transformed gamma distribution and loggamma distribution, respectively. (a) Calculate the mean of the loss. (b) Calculate the probability that the loss exceeds its mean. (c) Calculate the variance of the loss. 2. Let two independent random variables X 1 and X 2 have distributions F 1 and F 2 , re- spectively. Actuary A assumes that the loss of a portfolio is Y A and the distribu- tion of Y A is the average of the distributions F 1 and F 2 , namely, the cdf of Y A is F Y A ( y ) = 1 2 ( F 1 ( y ) + F 2 ( y )) for y ( -∞ , ), while actuary B assumes the loss of the same portfolio is Y B , which is the average of
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 2

Practice Questions 2 - Practice Questions 2 ACTSC 431/831...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online