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Student Solutions Manual to Accompany Loss Models: From Data to Decisions, Fourth Edition by Gordon E. Willmot, Harry H. Panjer, Stuart A. Klugman

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CHAPTER 18

CHAPTER 18

18.1   SECTION 18.9

18.1 The conditional distribution of X given that Y = y is

image

for x = 0, 1, 2,…, y. This is a binomial distribution with parameters m = y and q = λ1/(λ1 + λ2).

18.2

image

This is the hypergeometric distribution.

18.3 Using (18.3) and conditioning on N yields

image

For the variance, use (18.6) to obtain

image

18.4 (a) fX(0) = 0.3, fX(1) = 0.4, fX(2) = 0.3.

      fY(0) = 0.25, fY(1) = 0.3, fY(2) = 0.45.

(b) The following array presents the values for x = 0, 1, 2:

image

(c)

image

(d)

image

18.5 (a)

image

Now a normal density N(μ, σ2) has pdf image. Then fX|Y(x|y) ∝ f(x, y) is N  .

(b)

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