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 $110Y2. Calculate the expected amount of the surcharg.

A. The E (Y) is 0.80

B. The expected amount of the surcharges is $165

Step-by-step explanation:

A. In order to calculate the E (Y), we would have to calculate the following formula:

E (Y) = ∑yp (y)

E (Y) = (0*0.5) + (1*0.25) + (2*0.20) + (3*0.05)

E (Y) = 0+0.25+0.40+0.15

E (Y) = 0.80

B. In order to calculate the expected amount of the surcharges we would have to calculate the following formula:

E ($110Y∧2) = 110E (Y∧2)

=110∑y∧2p (y)

=110 ((0∧2*0.5) + (1∧2*0.25) + (2∧2*0.20) + (3∧2*0.05))

110 (0+0.25+0.80+0.45)

=$165