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.

y 0 1 2 3
p(y) 0.50 0.25 0.20 0.05

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

a. 0.80

b. $80

Step-by-step explanation:

a. The expected value, E(Y) is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)]. In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average:

Hence the expected value E(Y) is 0.80

b. From a above we have the expectation as  E(Y)=0.80.

-The expected amount is calculated by multiplying  expectation by the surcharge:

Hence, the expected amount of surcharge is $80