Violations 0 0 1 2 3 4 5 >5

Fine A$1000 0 0 10 10 10 20 50

(Please note from the table that 0 violations = 0 fines, 1 violation = 0 fines, 2 violations = $10,000 fine, 3 violations = $10,000 fine, 4 violations = $10,000 fine, 5 violations = $20,000 fine, More than 5 violations = $50,000 fine)

Violations are based on monthly data so the maximum number of violations in a year is 12. You believe that the probability of violation in any particular month is 0.2

(a) What is the probability that you will not pay any fine during the year?

(b) What must be assumed in order to answer (a)?

(c) Add a row with probabilities for each column

(d) What is the mean fine (i.e. expected value of the fine)?

(e) How much would the mean change if the maximum fine was doubled i.e. $100 instead of $50?

(f) Suppose that you violate at the first month. Even though you do not get fined for this directly, you are now more likely to face fines during the year.

Draw new table including the probabilities row.

(g) How much has the violation at the first month cost you?

Hint: how expected value of the fine has changed due to this violation

Fine A$1000 0 0 10 10 10 20 50

(Please note from the table that 0 violations = 0 fines, 1 violation = 0 fines, 2 violations = $10,000 fine, 3 violations = $10,000 fine, 4 violations = $10,000 fine, 5 violations = $20,000 fine, More than 5 violations = $50,000 fine)

Violations are based on monthly data so the maximum number of violations in a year is 12. You believe that the probability of violation in any particular month is 0.2

(a) What is the probability that you will not pay any fine during the year?

(b) What must be assumed in order to answer (a)?

(c) Add a row with probabilities for each column

(d) What is the mean fine (i.e. expected value of the fine)?

(e) How much would the mean change if the maximum fine was doubled i.e. $100 instead of $50?

(f) Suppose that you violate at the first month. Even though you do not get fined for this directly, you are now more likely to face fines during the year.

Draw new table including the probabilities row.

(g) How much has the violation at the first month cost you?

Hint: how expected value of the fine has changed due to this violation

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