An individual who has automobile insurance from a certain co

An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is the following.

(a) Compute E(Y).
E(Y) =

(b) Suppose an individual with Y violations incurs a surcharge of $100Y². Calculate the expected amount of the surcharge.
$

Solution

a)

E(Y) = y . p(y)

= 0 * 0.5 + 1 * 0.2 + 2 * 0.25 + 3 * 0.05

= 0.85

b)

E(100 Y^2) = 100 * 0.5 * 0^2 + 100 * 1^2 * 0.2 + 100 * 2^2 * 0.25 + 100 * 3^2 * 0.05

= 165