Question

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 y 0 1 2 3 4 p(y) 0.50 0.20 0.15 0.10 0.05 Suppose an individual with Y violations incurs a surcharge of 100Y 2 . Calculate the expected amount of the surcharge

Answer 1

1) The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1

2) The expected amount of surcharges is $250

Explanation:

Given that;

Y 0 1 2 3 4

p(y) 0.50 0.20 0.15 0.10 0.05

1)

Value of E(Y)

E(Y) = (0×0.50) + ( 1×0.20) + ( 2×0.15) + (3×0.10) + (4×0.05)

= 0 + 0.20 + 0.3 + 0.3 + 0.2

E(Y) = 1

Therefore, The expected value of the number of moving violations for which the individual was cited during the last 3 years is 1

b)

Suppose an individual with Y violations incurs a surcharge of $100Y² , the expected amount of the surcharge is given by,

E($100Y²) = 100E(Y)²

= 100∑Y²P(y)

= 100(0²×0.50) + ( 1²×0.20) + ( 2²×0.15) + (3²×0.10) + (4²×0.05)

= 100( 0 + 0.2 + 0.6 + 0.9 + 0.8 )

= 100(2.5)

= $250

Therefore; The expected amount of surcharges is $250