The probability distribution for collision insurance claims paid through the T. J. Automobile Insurance Company is as follows:
| Claim |
Probability |
| $0 |
0.90 |
| $500 |
0.04 |
| $1000 |
0.03 |
| $2000 |
0.01 |
| $3000 |
0.01 |
| $4000 |
0.01 |
a) Employ the expected collision claim amount to find out the collision insurance premium that would let the company to break even on collision portion of policy.
b) The insurance company charges the annual rate of $250 for collision coverage. Find out the expected value of collision policy for policy holder? Why does the policyholder buy the collision policy with this expected value?