Answer:
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
Step-by-step 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
