Chapter 4

Question 1

Y (amount that the insurer pays) = ? with d only

Answer 1

0, if x < or equals d
x-d, if x > d

Question 2

E(y) = ? with d only (discrete)

Answer 2

Sum of (x-d) ⋅ P(x = x)

Question 3

E(y^2) = ? with d only (discrete)

Answer 3

Sum of (x-d)^2 ⋅ P(x = x)

Question 4

E(y) = ? with d only (continuous)

Answer 4

Integral evaluated between infinity and d of (x-d) times f(x)
OR
Integral evaluated between infinity and d of S(x)

Question 5

E(y^2) = ? with d only (continuous)

Answer 5

intégrale évaluer entre infini et d de (x-d)^2 fois f(x)

Question 6

Shortcut E(y) = ? with d only (exponential and uniform)

Answer 6

E(y) = ((x-d) knowing x > d) ⋅ P(x > d)

Question 7

Z (Amount the insured pays) = ? with d only

Answer 7

x, if x < or equals d
d, if x > d

Question 8

Y = ? with u only

Answer 8

x, if x < or equals u
u, if x > u

Question 9

E(y) = ? with u only (discrete)

Answer 9

Sum of x ⋅P(x = x) + u ⋅ P(x > u)

Question 10

E(y^2) = ? with u only (discrete)

Answer 10

Sum of x^2 ⋅ P(x = x) + u^2 ⋅ P(x > u)

Question 11

E(y) = ? with u only (continuous)

Answer 11

Integral evaluated between u and 0 of x ⋅ f(x) dx + u ⋅ S_x(u)
OR
Integral evaluated between u and 0 of S(x)

Question 12

E(y^2) ? with u only, continuous

Answer 12

Integral evaluated between u and 0 of x^2 ⋅ f(x) dx + u^2 ⋅ S_x(u)

Question 13

Y = ? with u and d

Answer 13

0, if x < or equals d
(x - d), if d< x < d+u
u, si x > or equals d+u

Question 14

Coinsurance ?

Answer 14

% of loss the insurer reinburse. If only deductible or only limit, the function stays the same, but with a little a (between 0 and 1)

Question 15

Y = ? with a, d and u

Answer 15

0, if x < or equals d
a (x - d), if d < x < d + u/a
u, si x > or equals d+u/a

Question 16

E(y) = ? with a, u and d

Answer 16

Integral evaluated between d + u/a and d of a(x - d)⋅ f(x) dx + u ⋅ S_x(d + u/a)