Question

Accidental Death & Dismemberment Insurance covers accidents that results in death or loss of limbs due to accidents. Considering dismemberments only, let a discrete random variable X be the number of limbs lost from a policy holder in a given year.

Suppose that the probability distribution of X is x

0 p(x)=0.80

1 p(x)=0.13

2 p(x)=0.04

3 p(x)=0.02

4 p(x)=0.01

(a) Find the expected number of limbs lost for a randomly selected policy holder in a given year.

(b) suppose the insurance company pays $10,000 for loss of one limb, $20,000 for loss of two limbs, $50,000 for loss of three limbs, and $100,000 for loss of all limbs, how much should the annual premium be if the insurance company wants an average of $50 profit per policy holder? Hint: What is the expected insurance payment for an arbitrary policy holder?

Answer 1

a) E(x) =

So, 0.31 is the expected number of limbs lost for a randomly selected policy holder in a given year.

b)

E(cost) =

E(cost) = $4100

Company wants to make $50 profit per policy holder

So, annual premium = 4100 + 50 = $4160.