Question

Suppose that 10% of automobile accidents involve one car, 85% involve two, and 5% involve more than two. Suppose further that losses for these three types of accidents are uniformly distributed on [0, 5000], [0, 15000], and [0, 50000], respectively. (a) What is the expected loss of an automobile accident? (b) What is the variance in the loss?

Answer 1

Let X denotes the loss of a randomly selected automobile accident.

where X₁ : loss of an automobile accident that involve one car

X₂ : loss of an automobile accident that involve two cars

X₃ : loss of an automobile accident that involve more than two cars

Here,

that implies and

and

that implies and

and

that implies and

a) The expected loss of an automobile accident

B) The  variance in the loss