Chapter 4 Flashcards

1
Q

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

A

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

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2
Q

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

A

Sum of (x-d) ⋅ P(x = x)

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3
Q

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

A

Sum of (x-d)^2 ⋅ P(x = x)

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4
Q

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

A

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

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5
Q

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

A

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

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6
Q

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

A

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

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7
Q

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

A

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

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8
Q

Y = ? with u only

A

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

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9
Q

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

A

Sum of x ⋅P(x = x) + u ⋅ P(x > u)

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10
Q

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

A

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

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11
Q

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

A

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)

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12
Q

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

A

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

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13
Q

Y = ? with u and d

A

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

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14
Q

Coinsurance ?

A

% 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)

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15
Q

Y = ? with a, d and u

A

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

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16
Q

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

A

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