Chapter 4 Flashcards
Y (amount that the insurer pays) = ? with d only
0, if x < or equals d
x-d, if x > d
E(y) = ? with d only (discrete)
Sum of (x-d) ⋅ P(x = x)
E(y^2) = ? with d only (discrete)
Sum of (x-d)^2 ⋅ P(x = x)
E(y) = ? with d only (continuous)
Integral evaluated between infinity and d of (x-d) times f(x)
OR
Integral evaluated between infinity and d of S(x)
E(y^2) = ? with d only (continuous)
intégrale évaluer entre infini et d de (x-d)^2 fois f(x)
Shortcut E(y) = ? with d only (exponential and uniform)
E(y) = ((x-d) knowing x > d) ⋅ P(x > d)
Z (Amount the insured pays) = ? with d only
x, if x < or equals d
d, if x > d
Y = ? with u only
x, if x < or equals u
u, if x > u
E(y) = ? with u only (discrete)
Sum of x ⋅P(x = x) + u ⋅ P(x > u)
E(y^2) = ? with u only (discrete)
Sum of x^2 ⋅ P(x = x) + u^2 ⋅ P(x > u)
E(y) = ? with u only (continuous)
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)
E(y^2) ? with u only, continuous
Integral evaluated between u and 0 of x^2 ⋅ f(x) dx + u^2 ⋅ S_x(u)
Y = ? with u and d
0, if x < or equals d
(x - d), if d< x < d+u
u, si x > or equals d+u
Coinsurance ?
% 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)
Y = ? with a, d and u
0, if x < or equals d
a (x - d), if d < x < d + u/a
u, si x > or equals d+u/a