Exponential Mechanism: Query the most frequent Education result. Design an Exponential mecha

nism to ensure -differential privacy for the query. Repeat all the above procedures with = 0.5, 1.0.

1. 6 Points. In case of = 0.5, generate 1,000 results for the query over the original dataset, and

generate 1,000 results for the query over each of three other datasets: removing a record with the most

frequent Education; removing any record with the second most frequent Education; and removing

any record with the least frequent Education.

2. 6 Points. In each of the above 4 groups of 1,000 results, define a measure and utilize it to validate

that each of the last 3 groups of results and the original results are 0.5-indistinguishable.

3. 6 Points. Repeat all the above for = 1.0, utilize the above measure to validate that each of the last

3 groups of results and the original results are 1.0-indistinguishable.

4. 7 Points. Define another measure and utilize it to justify that the distortion of the 4,000 results for

= 1.0 is less than that of = 0.5.